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P_{n} the product of all positive integers x less than n

Source: IMO Shortlist 2004, number theory problem 6

June 14, 2005

modular arithmeticnumber theoryDivisibilityremainderIMO Shortlist

Problem Statement

Given an integer

{n>1}

, denote by

P_{n}

the product of all positive integers

x

less than

n

and such that

n

divides

{x^2-1}

. For each

{n>1}

, find the remainder of

P_{n}

on division by

n

.
Proposed by John Murray, Ireland