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odd prime: p \n(n+1)(n+2)(n+3)+1 for n iff p \ (m^2 - 5) for m

Source: Mexican Mathematical Olympiad 1993 OMM P6

July 29, 2018
number theoryprimeDivisibility

Problem Statement

pp is an odd prime. Show that pp divides n(n+1)(n+2)(n+3)+1n(n+1)(n+2)(n+3) + 1 for some integer nn iff pp divides m2āˆ’5m^2 - 5 for some integer mm.
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