Random Interesting Patterns Followed by Square Numbers
The square of...
Question
The square of any positive integer of the form 5q + 1 is of the same form. If true then enter 1 and if false then enter 0
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Solution
Let x be any positive integer of the form 5q + 1. When x =5q +1 x2=25q2+10q+1 x2=5q(5q+2)+1 Let m=q (5q +2). x2=5m+1 Hence, x2 is of the same form i.e. 5m + 1.