8.5

Part of 2021 Kyiv City MO Round 1

Problems(1)

Irreduced to ashes, modulo $p$

Source: Kyiv City MO 2021 Round 1, Problem 8.5

For a prime number

p > 3

, define the following irreducible fraction:

\frac{m}{n} = \frac{p-1}{2} + \frac{p-2}{3} + \ldots + \frac{2}{p-1} - 1

m

is divisible by

p

.
Proposed by Oleksii Masalitin

number theoryprime numbers