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"Fermat's factorization method" -wikipedia - Google Search
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name="sca_esv" value="23b5c302cf261505" type="hidden"/><input name="oq" type="hidden"/><input name="aqs" type="hidden"/><table class="cvifge"><tr><td class="O4cRJf"><input class="MhzMZd" value='"Fermat's factorization method" -wikipedia' name="q" type="text"/></td><td class="O1ePr"><input class="xB0fq" value="Search" type="submit"/></td></tr></table></form></div><div class="M7pB2"><table class="euZec"><tbody><tr><td class="EY24We"><span class="QIqI7">ALL</span></td><td><a class="CsQyDc" href="/search?q=%22Fermat%27s+factorization+method%22+-wikipedia&sca_esv=23b5c302cf261505&tbm=isch&source=lnms&sa=X&ved=0ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ_AUIBSgB">IMAGES</a></td><td><a class="CsQyDc" href="/search?q=%22Fermat%27s+factorization+method%22+-wikipedia&sca_esv=23b5c302cf261505&tbm=vid&source=lnms&sa=X&ved=0ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ_AUIBigC">VIDEOS</a></td><td><a class="CsQyDc" href="/search?q=%22Fermat%27s+factorization+method%22+-wikipedia&sca_esv=23b5c302cf261505&tbm=nws&source=lnms&sa=X&ved=0ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ_AUIBygD">NEWS</a></td></tr></tbody></table></div></div><div><div> <div> <div class="ezO2md"><div><div class="FYYwXe"> <div class="CSfvHb"> <span class="qXLe6d FrIlee"> <span class="fYyStc">Fermat's factorization method relies on the fact that </span> <span class="dloBPe fYyStc">every odd number can be represented as a difference of squares of two numbers</span> <span class="fYyStc">. That is, N = X ^ 2 - Y ^ 2 = (X + Y) * (X - Y). Here 'X' is greater than 'Y' and (x + y) and (x - y) are factors of N.</span> </span> </div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">27 Mar 2024</span> </span> </div> </div><div><a class="fuLhoc ZWRArf" href="/url?q=https://www.naukri.com/code360/library/fermat-s-factorization-method&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAcQAg&usg=AOvVaw0ACrMyQzHQYUn4-eWy81eC"><span class="CVA68e qXLe6d">Fermat's Factorization Method - Naukri Code 360</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">www.naukri.com › ... › Competitive Programming › Advanced Level</span> </span> </a></div><div class="oO6lG"> <span class="qXLe6d F9iS2e WMQ2Le"> <a class="M3vVJe" href="https://www.google.com/url?q=https://support.google.com/websearch%3Fp%3Dfeatured_snippets%26hl%3Den-SG&opi=89978449&usg=AOvVaw0XmUePKqidLOPpq7KneD4H">About featured snippets</a> </span> </div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://www.geeksforgeeks.org/fermats-factorization-method/&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAwQAg&usg=AOvVaw3ymAXULVjJ_2WjykE4obSv"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat's Factorization Method - GeeksforGeeks</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">www.geeksforgeeks.org › fermats-factorization-method</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">7 Jan 2024</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Fermat's Factorization method is based on the representation of an odd integer as the difference of two squares.</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://www.geeksforgeeks.org/fermats-factorization-method-for-large-numbers/&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECA0QAg&usg=AOvVaw0bSKRbJEqdWSe1_1sbb9w5"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat's Factorization method for large numbers - GeeksforGeeks</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">www.geeksforgeeks.org › fermats-factorization-method-for-large-numbers</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">24 Feb 2024</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Fermat's Factorization method is based on the representation of an odd integer as the difference of two squares.</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://math.stackexchange.com/questions/2597236/fermats-factorisation-method&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAkQAg&usg=AOvVaw3AZzHjfeFr5K_tddWtENHc"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat's factorisation method - prime numbers - Math Stack Exchange</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">math.stackexchange.com › questions › fermats-factorisation-method</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">8 Jan 2018</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Can Fermat's little theorem be used to list primes? 4 · Basic question on Fermat's factorization method · 1 · Numbers with special factorisation.</span> </span> <span class="qXLe6d FrIlee"> <a class="M3vVJe" href="/url?q=https://math.stackexchange.com/questions/1045976/basic-question-on-fermats-factorization-method&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQrAJ6BAgJEAY&usg=AOvVaw2T04XQDGCamllf7zzG7fti">Basic question on Fermat's factorization method</a> </span> <span class="qXLe6d FrIlee"> <a class="M3vVJe" href="/url?q=https://math.stackexchange.com/questions/211237/running-time-for-fermats-factorization-algorithm&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQrAJ6BAgJEAc&usg=AOvVaw2oPBKkjuR5gYrrrEDyCwoc">Running Time for Fermat's Factorization Algorithm</a> </span> <span class="qXLe6d FrIlee"> <a class="M3vVJe" href="/url?q=https://math.stackexchange.com/questions/1775067/factor-the-number-211-1-by-fermats-factorization-method&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQrAJ6BAgJEAg&usg=AOvVaw0SOsD5mGsAHEs9Gq7aTh08">Factor the number $2^{11} - 1$ by fermat's factorization method</a> </span> <span class="qXLe6d FrIlee"> <a class="M3vVJe" href="/url?q=https://math.stackexchange.com/questions/1142519/sieve-improvement-for-fermats-factorization-method&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQrAJ6BAgJEAk&usg=AOvVaw0CViCyk5tRlA3M2Eni-9s9">Sieve improvement for Fermat's factorization method</a> </span> <span class="qXLe6d FrIlee"> <a class="M3vVJe" href="/search?q=%22Fermat's+factorization+method%22+-wikipedia+site:math.stackexchange.com&sca_esv=23b5c302cf261505">More results from math.stackexchange.com</a> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://www.youtube.com/watch%3Fv%3DnGECWdjzX4A&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQtwJ6BAgFEAE&usg=AOvVaw0fnesaj5vlCGUys3Hr1iGW"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat Factorization Method - YouTube</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">www.youtube.com › watch</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc">Duration:</span> <span class="fYyStc"> </span> <span class="fYyStc YVIcad">8:56</span> <br/> <span class="fYyStc">Posted:</span> <span class="fYyStc"> </span> <span class="fYyStc YVIcad">30 Nov 2020</span> </span> </div> </div></td><td><div><a href="/url?q=https://www.youtube.com/watch%3Fv%3DnGECWdjzX4A&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQuAJ6BAgFEAI&usg=AOvVaw2wmlaW4uxLTln4kUQw7fXn"><table class="gNEi4d"><tbody><tr><td style="width:116px"> <div class="CO79Sb"> <img class="iUhyd" alt='Video for "Fermat's factorization method" -wikipedia' src="https://i.ytimg.com/vi/nGECWdjzX4A/default.jpg?sqp=-oaymwEECHQQQQ&rs=AMzJL3n2Br_JC8PxdByGymKAqj2sHaVeKg" style="width:116px;height:65px"/> </div> </td></tr><tr class="Y0aAmf FrIlee"><td><img src="//www.gstatic.com/ui/v1/icons/mail/images/triangle.gif" alt=""/> VIDEO</td></tr></tbody></table></a></div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://eprint.iacr.org/2023/026.pdf&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAoQAg&usg=AOvVaw2QBkf8A3dLP0YXvsV5vJoT"><span class="CVA68e qXLe6d fuLhoc ZWRArf">[PDF] Fermat Factorization in the Wild - Cryptology ePrint Archive</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">eprint.iacr.org › ...</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">8 Jan 2023</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">We also learned that Fermat's factorization method allows efficiently factoring a composite number composed of two close primes. 1A transcript ...</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://facthacks.cr.yp.to/fermat.html&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAsQAg&usg=AOvVaw1TDnSiQGho2e35P1TRqetl"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat's factorization method - FactHacks</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">facthacks.cr.yp.to › fermat</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">28 Dec 2012</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Fermat's factorization method factors N into p and q very quickly if p and q share half of their leading bits, ie, if the gap between p and q is below the ...</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://naturalnumbers.org/fixfermatfact.html&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAYQAg&usg=AOvVaw2RqnfLu6r3nIi3avf235zV"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fixing Fermat's Factorization Method - Natural Numbers</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">naturalnumbers.org › fixfermatfact</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">8 Nov 2009</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Fermat's factorization method says that by adding N to perfect squares (PSs) one will find eventually a sum N + PS that is itself a perfect square.</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://wiremask.eu/articles/fermats-prime-numbers-factorization/&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECAgQAg&usg=AOvVaw1cYrKPDzgemMDlkuGIWvJy"><span class="CVA68e qXLe6d fuLhoc ZWRArf">Fermat's factorization method - Wiremask</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">wiremask.eu › articles › fermats-prime-numbers-factorization</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc YVIcad">15 Oct 2016</span> <span class="fYyStc YVIcad"> · </span> <span class="fYyStc">Fermat's factorization method factors N into p and q very efficiently if p and q share half of their leading bits.</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div><a class="fuLhoc ZWRArf" href="/url?q=https://ijmttjournal.org/public/assets/volume-68/issue-1/IJMTT-V68I1P506.pdf&sa=U&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQFnoECA4QAg&usg=AOvVaw2mtID_DK1DoWMx-3iITWap"><span class="CVA68e qXLe6d fuLhoc ZWRArf">[PDF] Factors of Composite 4n2+1 using Fermat's Factorization Method</span> <span class="qXLe6d dXDvrc"> <span class="fYyStc">ijmttjournal.org › public › assets › volume-68 › issue-1</span> </span> </a></div><div class="Dks9wf"><table class="KZhhub"><tr><td class="udTCfd"><div> <div> <span class="qXLe6d FrIlee"> <span class="fYyStc">Abstract – In this article, we factor the composite 4n2 + 1 using Fermat's factorization method. Consequently, we characterized all proper factors of ...</span> </span> </div> </div></td></tr></table></div></div></div> </div> </div><div> <div> <div class="ezO2md"><div><div> <span class="qXLe6d x3G5ab"> <span class="dloBPe fYyStc">Related searches</span> </span> </div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat's+factorization+method+example&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAE"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat's factorization method example</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat's+factorization+method+example"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat+factorization+calculator&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAI"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat factorization calculator</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat+factorization+calculator"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat's+factorization+method+pdf&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAM"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat's factorization method pdf</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat's+factorization+method+pdf"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat+factorization+method&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAQ"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat factorization method</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat+factorization+method"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat's+theorem&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAU"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat's theorem</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat's+theorem"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat's+little+theorem&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAY"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat's little theorem</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat's+little+theorem"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=fermat+primality+test&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAc"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">fermat primality test</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=fermat+primality+test"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div><div><table class="VeHcBf"><tbody><tr><td><a class="ZWRArf" href="/search?sca_esv=23b5c302cf261505&q=sieve+of+eratosthenes&sa=X&ved=2ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQ1QJ6BAgEEAg"><span class="CVA68e qXLe6d"> <span class="qXLe6d FrIlee"> <span class="fYyStc">sieve of eratosthenes</span> </span> </span></a></td><td><div class="MGsU1d"><a href="/search?sca_esv=23b5c302cf261505&q=sieve+of+eratosthenes"><div class="FrIlee">></div></a></div></td></tr></tbody></table></div></div></div> </div> </div></div><table class="uZgmoc"><tbody><td><a class="frGj1b" href="/search?q=%22Fermat%27s+factorization+method%22+-wikipedia&sca_esv=23b5c302cf261505&ei=DxBIZ_XjGZuF4-EPweziuQc&start=10&sa=N">Next ></a></td></tbody></table><br/><div class="TuS8Ad" data-ved="0ahUKEwi1p724tf6JAxWbwjgGHUG2OHcQpyoIRQ"><style>.VYM29{font-weight:bold}</style><div class="HddGcc" align="center"><span class="VYM29">Singapore</span><span> - 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