Question

prove that the square of any positive integer of the form of 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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