Question

If $n$ is a positive integer, then $5^{2n+2}-24n-25$ is divisible by

• A. 574
• B. 575
• C. 675
• D. 674
• E. 576

Answer 1

Answer: (E)

Let $P(n)=5^{2n+2}-24n-25$
For $n=1,$ $p(1)=5^2-24-25=576$ $p(2)=5^6-24(2)-25=15552$
$=576\times 27$
Here, we see that $p(n)$ is divisible by 576.