MCQ
$25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by
- ✓$34$ but not by $14$
- Bboth $14$ and $34$
- Cneither $14$ nor $34$
- D$14$ but not by $34$
✓
Answer
Correct option: A.
$34$ but not by $14$
a
$25^{190}-8^{190}$ is divisible by $25-8=17$
$25^{190}-8^{190}$ 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 $8-2=6$
$L.C.M.$ of $1746=34$
$\therefore$ divisible by $34$ but not by $14$
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