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

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.


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