Determine all integer solutions of the equation \(3x - 12y = 7\).
Prove there are no integer solutions for the equation \(4^k - 4^l = 10^n\).
Let \(s\) and \(t\) be two positive integers. Can we have \(s^2=t^2+2\)?
Are there any two-digit numbers which are the product of their digits?
Find, with proof, all integer solutions of \(a^3+b^3=9\).