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7^(2n)+16n-1(n""inNN) is divisble by...

`7^(2n)+16n-1(n""inNN)` is divisble by

A

65

B

63

C

61

D

64

Text Solution

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If n is a positive integer (gt1) , show that, (4^(2n+2)-15n-16) is always divisible by 225.

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Knowledge Check

  • If p inNN then the expression p^(n+1)+(p+1)^(2n-1) is divisible by the expressions are -

    A
    `p^(2)+p+1`
    B
    `p^(2)+p`
    C
    `((p^(4)+p^(2)+1))/((p^(2)-p+1))`
    D
    `p^(2)+1`

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    Using binomial theorem for a positive integral index, prove that (2^(3n)-7n-1) is divisble by 49, for any positive integer n.

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