Discrete math

Question

Prove the following: $3 \; | \;\left ( a^2+b^2 \right )$ if and only if $3 \; | \;a$ and $3 \; | \;b$.

Comments

Wat does dis '|' symbol mean?

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"divides"

Answer 1

For any integer x

$x\%3 = 0\,\; or \;1 \, \, or\,\, 2$

$\therefore x^2\%3 = 0 \;\, or \;1 \; or \; 2^2 \;\%\,3=1$

$Thus \, a^2 +b^2 \;can \, be\,$

$0+0=0\; or\; 0+1=1 \;or\; 1+0=1.$

Thus the only possibility is when both $a$ and $b$ are divisible by 3.