4. Show that any positive integer is of the form 3 or 3q + 1 or 3q +2 for some integer q.
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let x be the integer
x=39
x²=9q?
x²=3(3q)
x²=3q [let 3q? be q]
x=3q+1
x²-(3q+1)? x²=9q?+6q+1
x²=3(3q?+2q)+1 x²-(3q+1) [let 3q?+2q be q]
x=3q+2 x²-(3q+2)?
x²=9q?+12q+4 x²=3(3q?+4q+1)+1
x²=(3q+1) [3q2+4q+1 be q]
it proves q? is in the form of 3q and (3q+1) but
not in the form of (3q+2)
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