MathDB

6

Part of 2012 QEDMO 11th

Problems(1)

1^{p-1} + 2^{p-1} +...+ (p-1)^{p-1} = p + (p-1)! \mod p^2

Source: 11th QEDMO p6 Seniors (6-8. 12. 2012) https://artofproblemsolving.com/community/c1512515_qedmo_200507

5/16/2021
Let pp be an odd prime number. Prove that 1p−1+2p−1+...+(p−1)p−1≡p+(p−1)!mod  p21^{p-1} + 2^{p-1} +...+ (p-1)^{p-1} \equiv p + (p-1)! \mod p^2
number theoryremainderSum of powers