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
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Euler's theorem
Summary
Euler's theorem is a theorem[1]. It ranks in the top 7% of theorem entities by monthly Wikipedia readership (306 views/month).[2]
Key Facts
- Euler's theorem's instance of is recorded as theorem[3].
- Leonhard Euler is named after Euler's theorem[4].
- Pierre de Fermat is named after Euler's theorem[5].
- Euler's theorem's part of is recorded as list of theorems[6].
- Euler's theorem's Freebase ID is recorded as /m/0j349[7].
- Euler's theorem's solved by is recorded as Leonhard Euler[8].
- Euler's theorem's defining formula is recorded as a^{\varphi(n)} \equiv 1 \pmod n[9].
- Euler's theorem's studied by is recorded as number theory[10].
- Euler's theorem's MathWorld ID is recorded as EulersTotientTheorem[11].
- Euler's theorem's maintained by WikiProject is recorded as WikiProject Mathematics[12].
- Euler's theorem's Microsoft Academic ID is recorded as 194672700[13].
- Euler's theorem's in defining formula is recorded as a[14].
- Euler's theorem's in defining formula is recorded as n[15].
- Euler's theorem's in defining formula is recorded as \varphi(n)[16].
- Euler's theorem's generalization of is recorded as Fermat's little theorem[17].
- Euler's theorem's Namuwiki ID is recorded as 오일러 정리[18].
- Euler's theorem's Treccani's Enciclopedia della Matematica ID is recorded as teorema-di-eulero-fermat[19].
- Euler's theorem's Metamath statement ID is recorded as eulerth[20].
Why It Matters
Euler's theorem ranks in the top 7% of theorem entities by monthly Wikipedia readership (306 views/month).[2] It has Wikipedia articles in 27 language editions, a strong signal of global cultural recognition.[21] It is known by 27 alternative names across languages and contexts.[22]