prove that the square of any positive integer is of the form 5q,5q+1,5q+4 for same integer q
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Let us Consider that a & b are two positive integers.
a = bm + r & 0 < r < b
b = 5 So, r can be 0, 1, 2, 3 & 4
a = 5m + r
If r = 0
a = 5m
If r = 1
If r = 2
If r = 3
If r = 4
Hence, Square of any positive integer is of the form 5q, 5q+1, 5q+4 for some integer q.
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