25^190-19^190-8^190+2^190 is divisible by :

Question

$25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by :

Accepted Answer

$25^{190}-8^{190}$ is divisible by $25-8=17$; $19^{190}-2^{190}$ is divisible by $19-2=17$.

$25^{190}-19^{190}$ is divisible by $25-19=6$; $8^{190}-2^{190}$ is divisible by $8-2=6$.

So the full expression is divisible by $	ext{lcm}(17,6)=102=17	imes6$, and specifically by $	ext{lcm}(17,2)=34$.

Divisible by 34 but not by 14

Solutions · 1