Find $x$.$$\left(2\cdot 7\right)^n+\left(3\cdot 5\right)^n-5 \equiv 0 \pmod{x},\quad n\in\mathbb{Z}$$

Question

anonymous · Answer

@KingGeorge

anonymous · Answer

@ishaan ayye konsa grade ka problem ha?

anonymous · Answer

hmm depends. what grade are you in?

anonymous · Answer

i 'm in 12th

anonymous · Answer

but i don't have any i idea how to solve this problem....can we solve with mathmetical induction

anonymous · Answer

you can try it then.

anonymous · Answer

hmm idk, i don't know how you could possibly solve it with mathematical induction.

hartnn · Answer

is the power in LHS 'n' ? because then LHS modx will give u LHS for any and every value of x(and quotient=0)...as LHS does not depend on x....

anonymous · Answer

yes, the exponential power is $n$ and $n\in \mathbb{Z}$.

experimentx · Answer

what is x? integer or real number?

anonymous · Answer

Integer.

anonymous · Answer

i think its$$2\times7^n+3\times 5^n-5 $$

anonymous · Answer

hmm maybe. i can't be sure of the question, i got it yesterday on my test. does it solves the problem? @mukushla

anonymous · Answer

yeah it solves the problem and answer will be  $x|24$...

anonymous · Answer

thanks. i got the same as well. i must have read the question wrong.

anonymous · Answer

very well...:)