Prove that the product of four consecutive natural numbers cannot be the square of an integer. So let n be a natural number. So f(n) = n(n+1)(n+2)(n+3) n --- 1 --- 2 --- 3 --- 4 --- 5 --- 10 f(n)-24--120-360-840-1080-17160 The conjecture I want to prove is F(n) + 1 is always a square. n(n+1)(n+2)(n+3) = (n2+3n)(n2+3n+1) so [(n2+3n-1)+1)][(n2+3n+1)-1]+1 and because a2-b2 = (a+b)(a-b) [(n2+3n+1)2-1)+1] = (n2+3n)2 So this proves that f(n) + 1 is in fact a square. My question is how does this prove that f(n) is NOT a square? I mean it seems obvious, but I am trying to learn to prove things.