g Prove that for any integer n, n is divisible by 3 iff n 2 is divisible by 3. Does your proof work for divisibility by 4 - why or why not? Identify the kind of proof steps you used, and why.

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Giana Boyer

Mathematics

25 May, 23:36

g Prove that for any integer n, n is divisible by 3 iff n 2 is divisible by 3. Does your proof work for divisibility by 4 - why or why not? Identify the kind of proof steps you used, and why.

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Ethan Paul · Answer 1

If n is devisible by 3 then n^2 is devisible by 3 it easy.

n=3k so n^2=9k so 9 is devisible by 3.

In the other way, if n^2 is devisible by 3we have n^2=3k wher k is integer number which has to be devisible by 3. If k is not devisible by 3, then n=/sqrt3*r, r^2=k. So n is not integer, contradiction.

This proof show us that iff doesnt work.

If n is devisile by 4 then n^2 is also devisible by 4. But if we have that n^2 is devisibke by 4 then n hasn't be devisible by 4. Example: n^2=36 is dev by 4 but n=6 is not dev by4.

Its allow because / sqrt 4 is 2.