1

Part of 1990 Nordic

Problems(1)

sum from k=1 to (n-1)^p, of k^m

Source: Nordic Mathematical Contest 1990 #1

m, n,

p

be odd positive integers. Prove that the number

\sum\limits_{k=1}^{{{(n-1)}^{p}}}{{{k}^{m}}}

is divisible by

n

number theorySum of powers