With respect to publishing or pre-print, or simply discussing with other mathematicians. How can one know if a result they have found is very useful or even interesting?
For example, I have found a general solution to the Prouhet Tarry-Escott problem similar to the Thue-Morse sequence related solution with $n=R^{k-1}(k-1)!$ for $R>2$. It also has the very nice property that the disjoint multisets $A$ and $B$ satisfy $x\in A \Rightarrow$ $(x\equiv 1 \mod R)$ and $x\in B \Rightarrow$ $(x\equiv -1 \mod R)$. A simple example for $R=4$ and $k=2$ is: $$1 + 5+5+5 = 3+3+3+7$$ $$1^{2} + 5^{2}+5^{2}+5^{2} = 3^{2}+3^{2}+3^{2}+7^{2}$$