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1+1/2+1/3+1/4+⋯+1/30+1/31 = I/31! Find the remainder when I is divided by 23

Автор: My One Fiftieth Of A Dollar

Загружено: 2025-11-24

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Wilson's Theorem an Excellent Modular Arithmetic Reduction Aid for this problem type.
Beginning number theory students may not understand that (p-1)! ≡ -1(mod p) is equivalent to (p-1)! ≡ p - 1(mod p) where p is a prime number. math stack exchange user/contributor evinda expounded on this equivalency July 2014. The easiest explanation of the equivalency is p ≡ 0 (mod p). Montreal mathematician Jonathan Love is interested in related number theoretic topics. Canadian mathematician Thomas Jeffery's generalization is a must read for much more depth and breadth!
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Read April 2023 aardwolfie of Reddit detailing math stack exchange lore and culture and avoidance of stating, speaking, or authoring unsolicited opinions.

1+1/2+1/3+1/4+⋯+1/30+1/31 = I/31!  Find the remainder when I is divided by 23

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