All Questions

Erdős and his coauthors often wrote about problems relating to the densities of sets of multiples. I have a computational question about the same topic. I have a finite* set $A=a_1<\cdots<a_r$ ...

Is there any way to find non-trivial solutions to the equation $x^2 + y^2 - x \equiv 0 \mod{N}$? There are clearly several trivial solutions, for example $(x, y) = (0, 0), (1, 0), (2^{-1}, 2^{-1}), (2^...

Let $n$ be integer with unknown factorization. Assume factoring $n$ is inefficient. Let $a,b,c$ satisfy $a^2+b^2 \equiv c^2 \bmod{n}, 0 \le a,b,c \le n-1$. Is it possibly to lift the above ...