Question

use euclid's division Lemma to show that the square of any positive integer is of the form 3p ,3p+1
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Answer 1

3p ....b = 3

r = 0

a = bq + r

a = 3q+0

s. b. s

a² = 9q²

a² = 3(3q²)

p= (3q²)

a² = 3p

3p+ 1

r = 1

a = bq +r

a = 3q +1

s. b. s

a² =( 3q +1)²

a² = 9q² + 6q +1

a² = 3(3q²+2q) +1

p = (3q² + 2q)....

a² = 3p +1