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Product divisble by p^3

Source: Tuymaada 2018 Senior League/Problem 5

July 20, 2018
number theorydivisibleprime numbers

Problem Statement

A prime pp and a positive integer nn are given. The product (13+1)(23+1)...((n−1)3+1)(n3+1)(1^3+1)(2^3+1)...((n-1)^3+1)(n^3+1) is divisible by p3p^3. Prove that p≤n+1p \leq n+1.
Proposed by Z. Luria
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