Prove that square of any positive integer is of the form 5q , 5q+1 ,5q+4 or 4q+1 for some integer q?
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by Euclid division algorithm a=bq+r
let a=5m
squaring on both sides we get
a²=25m²
a²=5(5m²)
a=5(q);q=5m²
like that same process for remaining 5q+1,5q+4,4q+1
let a=5m
squaring on both sides we get
a²=25m²
a²=5(5m²)
a=5(q);q=5m²
like that same process for remaining 5q+1,5q+4,4q+1
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