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Using binomial theorem, prove that 6^n-5...

Using binomial theorem, prove that `6^n-5n`always leaves remainder 1 when divided by 25.

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To prove that \( 6^n - 5n \) always leaves a remainder of 1 when divided by 25, we can use the Binomial Theorem. Here’s a step-by-step solution: ### Step 1: Rewrite \( 6^n \) We can express \( 6 \) as \( 1 + 5 \). Therefore, we can rewrite \( 6^n \) as: \[ 6^n = (1 + 5)^n \] ...
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Knowledge Check

  • The remainder when 6^(n) -5n is divided by 25 is

    A
    1
    B
    2
    C
    3
    D
    7

  • The remainder when 5^(4n) is divided by 13, is

    A
    1
    B
    8
    C
    9
    D
    10

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