Question

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

Answer 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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