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Ishaan94

  • 3 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
    • 3 years ago
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    @KingGeorge

  2. pawankumar
    • 3 years ago
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    @ishaan ayye konsa grade ka problem ha?

  3. Ishaan94
    • 3 years ago
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    hmm depends. what grade are you in?

  4. pawankumar
    • 3 years ago
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    i 'm in 12th

  5. pawankumar
    • 3 years ago
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    but i don't have any i idea how to solve this problem....can we solve with mathmetical induction

  6. Ishaan94
    • 3 years ago
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    you can try it then.

  7. Ishaan94
    • 3 years ago
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    hmm idk, i don't know how you could possibly solve it with mathematical induction.

  8. hartnn
    • 3 years ago
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    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
    • 3 years ago
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    yes, the exponential power is \(n\) and \(n\in \mathbb{Z}\).

  10. experimentX
    • 3 years ago
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    what is x? integer or real number?

  11. Ishaan94
    • 3 years ago
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    Integer.

  12. mukushla
    • 3 years ago
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    i think its\[2\times7^n+3\times 5^n-5 \]

  13. Ishaan94
    • 3 years ago
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    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
    • 3 years ago
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    yeah it solves the problem and answer will be \(x|24\)...

  15. Ishaan94
    • 3 years ago
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    thanks. i got the same as well. i must have read the question wrong.

  16. mukushla
    • 3 years ago
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    very well...:)

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