Question

prove if 3 | (a^2+b^2) then 3 | a and 3 | b

Answer 1

\[3n = a^2 + b^2 \iff 3n - a^2 = b^2 \iff 3\left(n-\dfrac{a^2}{3}\right) = b^2\]This means that \(a^2\) must be divisible by \(3\) (get why?) and if so, then \(b^2\) is also a multiple of \(3\). If \(3|a^2\) then \(3|a\) and \(3|b^2\) then \(3|b\).

Q.E.D.

Answer 2

what does Q.E.D. mean?

Answer 3

Proved.

Answer 4

thank you

Answer 5

You're welcome, I hope you get what my proof says :-)

Answer 6

I appreciate your work and if I wasn't able to read mathematical proofs I would not have made it this far.

Answer 7

Yay!