A Perfect Square

[BigGlenntheHeavy]

Show that the sum of 1 and the product of any four consecutive integers is a perfect square.

 

[Deleted member 4993]

Show that the sum of 1 and the product of any four consecutive integers is a perfect square.

Spoiler: :26ffga3c

(n-1)n(n+1)(n+2) + 1 = n[sup:26ffga3c]4[/sup:26ffga3c] + 2n[sup:26ffga3c]3[/sup:26ffga3c] - n[sup:26ffga3c]2[/sup:26ffga3c] - 2n + 1 = (n[sup:26ffga3c]2[/sup:26ffga3c] + n - 1)[sup:26ffga3c]2[/sup:26ffga3c][/spoiler:26ffga3c]

 

[Denis]

Show that the sum of 1 and the product of any four consecutive integers is a perfect square.

Please show your work. Homework not done here (except by Mr Khan!)