Question

Show that any positive integer is of the form 3q, 3q+1, 3q+2, where q is some integer

Answer 1

let x be the integer
x=3q
x²=9q²
x²=3(3q²)
x²=3q [let 3q² be q]
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x=3q+1
x²=(3q+1)²
x²=9q²+6q+1
x²=3(3q²+2q)+1
x²=(3q+1) [let 3q²+2q be q]
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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]
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it proves q² is in the form of 3q and (3q+1) but not in the form of (3q+2)

Answer 2

Here's your answer......