Prove that square of any positive integer of the form 5q + 1 is of the – InterviewSolution

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1.

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

Answer»

Here, the integer ‘n’ is of the form 5q+1.

⇒ n= 5q+1

On squaring it,

⇒ n²= (5q+1)²

⇒ n²= (25q²+10q+1)

⇒ n²= 5(5q²+2q)+1

⇒ n²= 5m+1, where m is some integer. [For m = 5q²+2q]

Therefore, the square of any positive integer of the form 5q + 1 is of the same form.

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