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from <a href="/w/index.php?title=Red_auxiliary_numbers&redirect=no" class="mw-redirect" title="Red auxiliary numbers">Red auxiliary numbers</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In the study of <a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">ancient Egyptian mathematics</a>, <b>red auxiliary numbers</b> are numbers written in red ink in the <a href="/wiki/Rhind_Mathematical_Papyrus" title="Rhind Mathematical Papyrus">Rhind Mathematical Papyrus</a>, apparently used as aids for arithmetic computations involving <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fractions</a>.It is considered to be the first examples of method that uses <a href="/wiki/Least_common_multiple" title="Least common multiple">Least common multiples</a>. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Red_auxiliary_number&action=edit&section=1" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFGillings1982" class="citation book cs1">Gillings, Richard J. (1982). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/mathematicsintim0000gill"><i>Mathematics in the Time of the Pharaohs</i></a></span>. <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486243153" title="Special:BookSources/9780486243153"><bdi>9780486243153</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/301431218">301431218</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+in+the+Time+of+the+Pharaohs&rft.pub=Dover+Publications&rft.date=1982&rft_id=info%3Aoclcnum%2F301431218&rft.isbn=9780486243153&rft.aulast=Gillings&rft.aufirst=Richard+J.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmathematicsintim0000gill&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARed+auxiliary+number" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFClagett1989" class="citation book cs1"><a href="/wiki/Marshall_Clagett" title="Marshall Clagett">Clagett, Marshall</a> (1989). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_8c10QYoGa4UC"><i>Ancient Egyptian Science: Ancient Egyptian mathematics</i></a>. <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780871692320" title="Special:BookSources/9780871692320"><bdi>9780871692320</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/313400062">313400062</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Ancient+Egyptian+Science%3A+Ancient+Egyptian+mathematics&rft.pub=American+Philosophical+Society&rft.date=1989&rft_id=info%3Aoclcnum%2F313400062&rft.isbn=9780871692320&rft.aulast=Clagett&rft.aufirst=Marshall&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_8c10QYoGa4UC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARed+auxiliary+number" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBuntJonesBedient2012" class="citation book cs1">Bunt, Lucas N. H.; Jones, Phillip S.; Bedient, Jack D. (2012). <i>The Historical Roots of Elementary Mathematics</i>. <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780486139685" title="Special:BookSources/9780486139685"><bdi>9780486139685</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/868272907">868272907</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Historical+Roots+of+Elementary+Mathematics&rft.pub=Dover+Publications&rft.date=2012&rft_id=info%3Aoclcnum%2F868272907&rft.isbn=9780486139685&rft.aulast=Bunt&rft.aufirst=Lucas+N.+H.&rft.au=Jones%2C+Phillip+S.&rft.au=Bedient%2C+Jack+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ARed+auxiliary+number" class="Z3988"></span></li></ul> 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class="navbox-abovebelow" colspan="3" style="background-color:#decd87"><div> <ul><li><a href="/wiki/Glossary_of_ancient_Egypt_artifacts" title="Glossary of ancient Egypt artifacts">Glossary of artifacts</a></li> <li><a href="/wiki/Index_of_ancient_Egypt%E2%80%93related_articles" title="Index of ancient Egypt–related articles">Index</a></li> <li><a href="/wiki/Portal:Ancient_Egypt/Main_topics" title="Portal:Ancient Egypt/Main topics">Main topics</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;padding-left:81px"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ancient_Egyptian_agriculture" title="Ancient Egyptian agriculture">Agriculture</a></li> <li><a href="/wiki/Ancient_Egyptian_architecture" title="Ancient Egyptian architecture">Architecture</a> <ul><li><a href="/wiki/Egyptian_Revival_architecture" title="Egyptian Revival architecture">Revival</a></li> <li><a href="/wiki/List_of_Egyptian_obelisks" title="List of Egyptian obelisks">Obelisks</a></li> <li><a href="/wiki/Pylon_(architecture)" title="Pylon (architecture)">Pylon</a></li></ul></li> <li><a href="/wiki/Art_of_ancient_Egypt" title="Art of ancient Egypt">Art</a> <ul><li><a href="/wiki/Portraiture_in_ancient_Egypt" title="Portraiture in ancient Egypt">Portraiture</a></li></ul></li> <li><a href="/wiki/Egyptian_astronomy" title="Egyptian astronomy">Astronomy</a></li> <li><a href="/wiki/Egyptian_chronology" title="Egyptian chronology">Chronology</a></li> <li><a href="/wiki/Urban_planning_in_ancient_Egypt" title="Urban planning in ancient Egypt">Cities</a> <ul><li><a href="/wiki/List_of_ancient_Egyptian_towns_and_cities" title="List of ancient Egyptian towns and cities">List</a></li></ul></li> <li><a href="/wiki/Clothing_in_ancient_Egypt" title="Clothing in ancient Egypt">Clothing</a></li> <li><a href="/wiki/Ancient_Egyptian_race_controversy" title="Ancient Egyptian race controversy">Ancient Egyptian race controversy</a></li> <li><a href="/wiki/Population_history_of_Egypt" title="Population history of Egypt">Population history of Egypt</a></li> <li><a href="/wiki/Prehistoric_Egypt" title="Prehistoric Egypt">Prehistoric Egypt</a></li> <li><a href="/wiki/Ancient_Egyptian_cuisine" title="Ancient Egyptian cuisine">Cuisine</a></li> <li><a href="/wiki/Dance_in_ancient_Egypt" title="Dance in ancient Egypt">Dance</a></li> <li><a href="/wiki/Dynasties_of_ancient_Egypt" title="Dynasties of ancient Egypt">Dynasties</a></li> <li><a href="/wiki/Ancient_Egyptian_funerary_practices" title="Ancient Egyptian funerary practices">Funerary practices</a></li> <li><a href="/wiki/Category:Geography_of_ancient_Egypt" title="Category:Geography of ancient Egypt">Geography</a></li> <li><a href="/wiki/Great_Royal_Wife" title="Great Royal Wife">Great Royal Wives</a> <ul><li><a href="/wiki/List_of_ancient_Egyptian_royal_consorts" title="List of ancient Egyptian royal consorts">List</a></li></ul></li> <li><a href="/wiki/Egyptian_hieroglyphs" title="Egyptian hieroglyphs">Hieroglyphs</a> <ul><li><a href="/wiki/Cursive_hieroglyphs" title="Cursive hieroglyphs">Cursive hieroglyphs</a></li></ul></li> <li><a href="/wiki/History_of_ancient_Egypt" title="History of ancient Egypt">History</a></li> <li><a href="/wiki/Egyptian_language" title="Egyptian language">Language</a> <ul><li><a href="/wiki/Demotic_(Egyptian)" title="Demotic (Egyptian)">Demotic</a></li> <li><a href="/wiki/Hieratic" title="Hieratic">Hieratic</a></li></ul></li> <li><a href="/wiki/Ancient_Egyptian_literature" title="Ancient Egyptian literature">Literature</a></li> <li><a href="/wiki/Ancient_Egyptian_mathematics" title="Ancient Egyptian mathematics">Mathematics</a></li> <li><a href="/wiki/Ancient_Egyptian_medicine" title="Ancient Egyptian medicine">Medicine</a></li> <li><a href="/wiki/Military_of_ancient_Egypt" title="Military of ancient Egypt">Military</a></li> <li><a href="/wiki/Music_of_Egypt" title="Music of Egypt">Music</a></li> <li><a href="/wiki/Egyptian_mythology" title="Egyptian mythology">Mythology</a></li> <li><a href="/wiki/List_of_ancient_Egyptians" title="List of ancient Egyptians">People</a></li> <li><a href="/wiki/Pharaoh" title="Pharaoh">Pharaohs</a> <ul><li><a href="/wiki/List_of_pharaohs" title="List of pharaohs">List</a></li> <li><a href="/wiki/Ancient_Egyptian_royal_titulary" title="Ancient Egyptian royal titulary">Titulary</a></li></ul></li> <li><a href="/wiki/Ancient_Egyptian_philosophy" title="Ancient Egyptian philosophy">Philosophy</a></li> <li><a href="/wiki/Ancient_Egyptian_pottery" title="Ancient Egyptian pottery">Pottery</a></li> <li><a href="/wiki/Ancient_Egyptian_religion" title="Ancient Egyptian religion">Religion</a></li> <li><a href="/wiki/List_of_ancient_Egyptian_scribes" title="List of ancient Egyptian scribes">Scribes</a></li> <li><a href="/wiki/List_of_ancient_Egyptian_sites" title="List of ancient Egyptian sites">Sites</a> <ul><li><a href="/wiki/List_of_historical_capitals_of_Egypt" title="List of historical capitals of Egypt">Capitals</a></li> <li><a href="/wiki/Nome_(Egypt)" title="Nome (Egypt)">District</a></li></ul></li> <li><a href="/wiki/Ancient_Egyptian_technology" title="Ancient Egyptian technology">Technology</a></li> <li><a href="/wiki/Ancient_Egyptian_trade" title="Ancient Egyptian trade">Trade</a></li> <li><a href="/wiki/Egypt%E2%80%93Mesopotamia_relations" title="Egypt–Mesopotamia relations">Egypt–Mesopotamia relations</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="2" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/Giza_pyramid_complex" title="Giza pyramid complex"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/All_Gizah_Pyramids.jpg/100px-All_Gizah_Pyramids.jpg" decoding="async" width="100" height="66" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/All_Gizah_Pyramids.jpg/150px-All_Gizah_Pyramids.jpg 1.5x, 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