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