Exams › JEE Main › Maths
For a positive integer n, the expression 5^(2n+2) − 24n − 25 is divisible by which of the following?
- 574
- 575
- 674
- 576
Correct answer: 576
Solution
5^(2n+2)-24n-25 = 25*25^n -24n -25 = 25(25^n-1) -24n. Since 25^n-1 = (25-1)(...) = 24k, write 25(25^n-1)-24n; checking n=1 gives 576, n=2 gives 15552 = 27*576, etc. The expression is always divisible by 576.
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