prove that the square of any positive integer of form 5q+1 is of the same form​

1 thought on “prove that the square of any positive integer of form 5q+1 is of the same form​”

1. Answer: Let n = 5q + 1 where q is a positive integer

   ∴ n2 = (5q + 1)2

   = 25q2 + 10q + 1

   = 5(5q2 + 2q) + 1

   = 5m + 1, where m is some integer

   Hence, the square of any positive integer of the form 5q + 1 is of the same form.

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