Question

by Euclid alogarithm prove that square of any positive integer is of the form 3p,3p+1

Answer 1

r = 0,1,2
integer be a=bq+r

r=0

a = (3q+0)² = 9q² = 3p where p = 3q²
a = (3q+1)² = 9q² +1 + 6q = 3p+1 where p = 3q² +2q
a= (3q+2)² = 9q² + 4 + 12q = 3p+1 where p = 3q² +1 +4q

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