Q62 / 170 · Manipal (MET) 2018 · Mathematics

The statement $P(n)=9^n-8^n$, when divided 8 , always leaves the remainder

  • Correct answer
    A
    1
  • B
    2
  • C
    3
  • D
    7

Solution

Given, $P(n)=9^n-8^n$ $\therefore \quad P(1)=9-8=1$ $\therefore \quad P(\mathrm{l})-\mathrm{l}=0$, which is divisible by 8 . Now, $P(2)=9^2-8^2=17$ When divided by 8 , it leaves the remainder 1 .

Hence, the correct answer is option: 'A'.

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