Prove that the square of a positive integer is of form 5q+1

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Solution

Our integer is 5q+1
Squaring it, we get (5q+1)^2 = 25q^2 + 10q +1
= 5(5q^2 + 2q) +1
= 5m+1 : which is in the same form as the integer with which we started!

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