JEE 2023 — Mathematics PYQ

The given expression is divisible by $6$ and $17$.

Also, $25^{190}-8^{190}$ is not divisible by $7$

but $19^{190}-2^{190}$ is divisible by $7$,

So, $25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by $34$ but not by $14$.