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If p be a natural number, then prove tha...

If p be a natural number, then prove that, `p^(n+1)+(p+1)^(2n-1)` is divisible by `(p^(2)+p+1)` for every positive integer n.

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`(p^(2)+p+1)` for every positive integer n
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CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Sample Questions for Competitive Exams
  1. If p be a natural number, then prove that, p^(n+1)+(p+1)^(2n-1) is div...

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  2. If for all ninNN and nge1, then (3^(2^(n))-1) is always divisible by

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  3. If ninNN , both expression n(n+1)(n+2) and n(n+1)(n+5) are multiple of...

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  4. The value of n for which n!gt2^(n) will true, are -

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  5. If n is even then the expression n(n^(2)+20) is divisible by the numbe...

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  6. If p inNN then the expression p^(n+1)+(p+1)^(2n-1) is divisible by the...

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  7. 10^(n)+3*4^(2)+5 is always divisible by the number -

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  8. 3^(2n) when divided by 8 leves the remainder-

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  9. If n be a positive integer, then the digit in the unit's place of 3^(2...

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  10. For a positive integer n,n(n+1)(2n+1) when divided by 6 leaves the rem...

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  11. ninNN,(n+1)^(3)+(n+2)^(3)+(n+3)^(3) when divided by 9, then the remain...

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  12. Match the entries given in left column with those given in right colum...

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  13. Match the entries given in left column with those given in right colum...

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  14. P(n):11^(n+2)+1^(2n+1) where n is a positive integer p(n) is divisib...

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  15. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If P(n) = 14642...

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  16. P(n):11^(n+2)+1^(2n+1) where n is a positive integer If n=3, then th...

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  17. If n be a positive integer and P(n):4^(5n)-5^(4n) P(n) is divisible ...

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  18. If n be a positive integer and P(n):4^(5n)-5^(4n) If P(n) be negativ...

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  19. If n be a positive integer and P(n):4^(5n)-5^(4n) When n=3 then the ...

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  20. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

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  21. Statement - I : For every natural number ((n+4)!)/((n+1)!) is divisibl...

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