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

Question

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

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Jasmine 2 months 2021-07-27T15:38:14+00:00 1 Answers 0 views 0

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    2021-07-27T15:39:23+00:00

    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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