MathDB

7

Part of 2016 Indonesia MO

Problems(1)

r_1+r_2+r_3+...+r_{p-1}=\frac{p^2(p-1)}{2} where r_k = remainder k^p : p^2

Source: Indonesia MO (INAMO) 2016 P7

9/14/2018
Suppose that p>2p> 2 is a prime number. For each integer k=1,2,...,p−1k = 1, 2,..., p-1, denote rkr_k as the remainder of the division kpk^p by p2p^2. Prove that r1+r2+r3+...+rp−1=p2(p−1)2r_1+r_2+r_3+...+r_{p-1}=\frac{p^2(p-1)}{2}
number theoryremainderSum