Is $x^y$ - $a^b$ divisible by $z$, where $y$ is large? The exact problem I'm looking at is:
Is $4^{1536} - 9^{4824}$ divisible by $35$?
But in general, how do you determine divisibility if the exponents are large?

You can use binomial theorem to break up the individual bases into multiples of the divisor and then you can expand binomially to check divisibilty. This is in a general case of doing such a problem . There may be more methods of doing such a problem.
