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

MCQ

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

✓
$34$ but not by $14$
B
both $14$ and $34$
C
neither $14$ 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 $25-8=17$

$19^{190}-2^{190}$ 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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