Find positive integer $x,y$ such that $7^{x}-3^{y}=4$ Find all positive integers $x,y$ such that $7^{x}-3^{y}=4$.
It is the problem I think it can be solve using theory of congruency. But I can't process somebody please help me .
Thank you 

If you take this equation mod 7 and mod 3, it becomes clearer:
$$ 7^x-3^y \equiv 4 \mod 7 \implies -3^y \equiv 4 \mod 7 $$
$$ 7^x-3^y \equiv 4 \mod 3 \implies 7^x \equiv 4 \mod 3 $$
This isolates the variables. You can either use Chinese Remainder Theorem or convert the new modular equations to normal equations to continue (as far as I can see).
