Question

show that any positive integer is of the form 3q or, 3+1 or, 3q + 2 for some integer 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)

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