Is the sum of the product of four continuous positive integers and 1 necessarily a complete square? Proof + example,

The sum of the product of four continuous positive integers and 1 must be a complete square number. Proof: let four continuous positive integers be n, N + 1, N + 2, N + 3 (where n is a positive integer) n (n + 1) (n + 2) (n + 3) + 1 = [n (n + 3)] [(n + 1) (n + 2)] + 1 = (n & # 178; + 3n) (n & # 178; + 3N + 2) + 1 = (n & # 178; + 3n) &# 178; + 2 (n & # 178; +

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1. Try to prove that the product of four continuous positive integers plus 1 must be a complete square? (write the proof and steps)
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