How do I solve $ 7^{a}+1 =3^{b}+5^{c} $ for natural $a$,$b$ and $c$?All I got after some modular arithmetic is that the $a$,$b$ and $c$ are all odd.The problem was posted on Art of Problem Solving(with no responses till now) and is supposedly from India International Mathematical Olympiad Training Camp.I was wondering if someone could please shed some insight as to whether it can be solved.
Thanks.(I am a bit skeptical about this problem although I may be wrong)