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## Ishaan94 2 years ago Find $$x$$.$\left(2\cdot 7\right)^n+\left(3\cdot 5\right)^n-5 \equiv 0 \pmod{x},\quad n\in\mathbb{Z}$

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1. Ishaan94

@KingGeorge

2. pawankumar

@ishaan ayye konsa grade ka problem ha?

3. Ishaan94

hmm depends. what grade are you in?

4. pawankumar

i 'm in 12th

5. pawankumar

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

6. Ishaan94

you can try it then.

7. Ishaan94

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

8. hartnn

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....

9. Ishaan94

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

10. experimentX

what is x? integer or real number?

11. Ishaan94

Integer.

12. mukushla

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

13. Ishaan94

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

14. mukushla

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

15. Ishaan94

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

16. mukushla

very well...:)

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