In the period of finals ( and studying for finals ) yahoo answers have been flooded with homework and assignment problems 99.9% involve mundane “plug it into a formula” type of solutions. As such, these are of no particular interest to me or for this series. Hopefully, now that most students swapped book for beaches, there will be more interesting questions posted. Meanwhile, here are two short problems I picked some time ago
Problem: Prove that if is relatively prime to and ,then
Solution: Using it follows
Since is relatively prime to we know that
and it must be true that
Problem: If and prove .
Solution: Since we know that for some . Similarly, for some . Notice, that both and must be odd. If, lets say, were even, then for some . But then and so .
Using and we have . But since both and are odd, their sum is even, i.e.
It now follows that