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(n+k)^2+1 divides factorial

Source: Romanian 2018 TST Day 1 Problem 4

May 25, 2020
number theorypell equationSophie Germain identityfactorial

Problem Statement

Given an non-negative integer kk, show that there are infinitely many positive integers nn such that the product of any nn consecutive integers is divisible by (n+k)2+1(n+k)^2+1.
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