Question

Prove that the product of 4 consecutive integers is 1 less than a perfect square.

Answer 1

what have you tried?

Answer 2

oops type-0! :(
\[n(n+1)(n+2)(n+3)\]

Answer 3

Tried many things in vain

Answer 4

Kidds stuffs,

Let the consecutive integers be \( (n - 1), n, (n + 1), (n + 2) \)

Expanding: \[n^4 + 2n^3 - n^2 - 2n= (n^2 + n - 1)^2-1 \]

Answer 5

Nice work ffm!