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Prove that the Square of Any Positive Integer of the Form 5q + 1 is of the Same Form. - Mathematics

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

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.1 | Q 6 | Page 10
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