Euler's theorem
generalization of Fermat's little theorem, that given coprime positive integers 𝑛 and 𝑎, then the φ(𝑛)-th power of 𝑎 is congruent to 1 modulo 𝑛, where φ is Euler’s totient function
| rdfs:label |
"Euler's theorem"@en
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skos:alt |
"Euler's totient theorem"@en
"Fermat–Euler theorem"@en
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| schema:description |
"generalization of Fermat's little theorem, that given coprime positive integers 𝑛 and 𝑎, then the φ(𝑛)-th power of 𝑎 is congruent to 1 modulo 𝑛, where φ is Euler’s totient function"@en
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schema:date |
"2026-06-29T11:38:51+00:00"^^xsd:dateTime |
| schema:version | 2511796387 |
| wikibase:identifiers | 6 |
| wikibase:sitelinks | 40 |
| wikibase:statements | 18 |
| p:P1136 | wd:statement/Q193910-a7a2425c-4fda-c60c-3a06-1eb7d887e2fb |
| p:P12888 | wd:statement/Q193910-9DF48EDE-17DA-486E-B976-2860C588D375 |
| p:P138 | wd:statement/Q193910-03026623-489b-f125-db18-47fa1f0d6a6f |
| wd:statement/Q193910-20d7c091-466b-eb19-83c5-680ae9b1f0dc | |
| p:P2534 | wd:statement/Q193910-5486fbb0-4f9b-5972-1409-2add4568fecf |
| p:P2579 | wd:statement/Q193910-ce27e350-495a-87ae-28c3-19ecb307f876 |
| p:P2812 | wd:statement/Q193910-0A567854-D89C-4EC1-893B-62FAEF705345 |
| p:P31 | wd:statement/Q193910-E6E68908-1A58-4993-BABB-D710B5A51D44 |
| p:P361 | wd:statement/Q193910-E55F21AB-C82E-4B69-A83F-7E9C82E71DE3 |
| p:P6104 | wd:statement/Q193910-0F75C556-C093-4EC0-8CF9-25242DEB0DBE |
| p:P6366 | wd:statement/Q193910-57B06509-8F8E-47B6-8FC9-479BC1BC6C4E |
| p:P646 | wd:statement/Q193910-8A673CDA-67D0-4736-BA4A-42E5B31D2FFA |
| p:P7235 | wd:statement/Q193910-1b7fdda0-44fc-d9f5-d686-eda3a6c851de |
| wd:statement/Q193910-24134a38-400c-c98f-d7d4-1a25bb4f5a3e | |
| wd:statement/Q193910-b0ce4976-4e79-cafa-53f1-5663d5412f1a | |
| p:P7719 | wd:statement/Q193910-5c2efd17-4f53-52e0-2d9e-e9be1400a5b9 |
| p:P8885 | wd:statement/Q193910-f4300f5a-4e73-2598-6fe0-e94ced647629 |
| p:P9621 | wd:statement/Q193910-9b714d39-4a4e-6588-e749-a0a5569b8c7f |
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p:direct- |
<https:/ |
| wdt:P1136 | Leonhard Euler |
| wdt:P12888 | "eulerth" |
| wdt:P138 | Pierre de Fermat |
| Leonhard Euler | |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>φ</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mrow></msup><mo stretchy="false">≡</mo><mn>1</mn><mrow data-mjx-texclass="ORD"><mspace width="0.444em"></mspace><mo stretchy="false">(</mo><mi>mod</mi><mspace width="0.333em"></mspace><mi>n</mi><mo stretchy="false">)</mo></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | number theory |
| wdt:P2812 | "EulersTotientTheorem" |
| wdt:P31 | theorem |
| wdt:P361 | list of theorems |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "194672700" |
| wdt:P646 | "/m/0j349" |
| wdt:P7235 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>φ</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>n</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P7719 | Fermat's little theorem |
| wdt:P8885 | "오일러 정리" |
| wdt:P9621 | "teorema-di-eulero-fermat" |
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