Prove: The square of a number that is
two more than a multiple of 3 is one more
than a multiple of 3.
(3n + 2)2 = 9n2 + 12n +4
= [ ? ]n2 + ]n+ ] +1
= [ [ ]n2 + [ ]n + 1) + 1
= 1 more than a multiple of 3