Originally Posted By Marksman762: I could use a little help with the following problem: We have to prove that 12, 13, 21, and 31 are the only doubledigit numbers whose squares are the reverses of the squares of the reverses of doubledigit numbers, specifically the aforementioned numbers. Both show why it works for these numbers, and that only these numbers work this way. Anyone have an idea? Thanks

Okay, this is fairly easy.
1. Take 12x12 = 144, 21x21 = 441 (441 = Reverse 144) (21 = reverse 12)
2. Take 13x13 = 169, 31x31 = 961 (31x31, again the reverse)
And so on.
The same works for 21 and 31 as they are only the revereses of 12 and 13, the ones we already did.
IM me if you have trouble understanding.
EDIT: To prove that take two random numbers and do the same operation and show that they are not reversable.