Question

Prove that the square of any positive integer of the form 5q + 1 is of the same form.

Answer 1

Let N = 5p + 1.

Then,

According to the condition:

N2 = 25p2 + 10p + 1 ⇒ 5(5p2 + 2p) + 1 ⇒ 5A+1

Where A = 5p2 + 2p

Therefore N2 is of the form 5m + 1.