Question

show that the positive integer is of the form 3q or 3q+1 or 3q+2 for some intever q​

Answer 1

Answer:

let x be the integer

x=3q

x²=9q²

x²=3(3q²)

x²=3q [let 3q² be q]

============================================

x=3q+1

x²=(3q+1)²

x²=9q²+6q+1

x²=3(3q²+2q)+1

x²=(3q+1) [let 3q²+2q be q]

============================================

x=3q+2

x²=(3q+2)²

x²=9q²+12q+4

x²=3(3q²+4q+1)+1

x²=(3q+1) [3q²+4q+1 be q]

=============================================

it proves q² is in the form of 3q and (3q+1) but not in the form of (3q+2)