ABC Conjecture: $ABC=2^m{p}^n{q}^r$ with Fermat or Mersenne Primes

Anupam Saxena

For $p$ and $q$ any two distinct Fermat or Mersenne primes, $m,n,r$ as positive integers and $\hat{I}¼=\pm 1$ satisfying any diophantine relation, $\mbox{(i)}\; 2^m + μ= p^nq^r, \mbox{…