MathDB

Classic Number Theory

Source: 1997 Korea National Olympiad #4

March 18, 2018

number theoryprime numbers

Problem Statement

For any prime number

p>2,

and an integer

a

and

b,

1+\frac{1}{2^3}+\frac{1}{3^3}+\cdots+\frac{1}{(p-1)^3}=\frac{a}{b},

prove that

a

is divisible by

p.