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Olympiad workbookIOQMBinomial Theorem

The number obtained by taking the last two digits of 5²⁰²⁴ in the same order is:

Correct answer

25

Step-by-step solution

Last two digits of 5²⁰²⁴ aligned & 5²⁰²⁴ a( 100) & 5^4 25( 100) & 5²⁰²⁴ 25( 100) aligned last 2 digits in same order is 25

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Find the largest positive integer n < 30 such that 1 2 (n^8+3 n^4-4 ) is not divisible by the square of any prime number.Let F_k(a, b)=(a+b)^k-a^k-b^k and let S= 1,2,3,4,5,6,7,8,9,10 . For how many ordered pairs (a, b) with a, b S and a b is F₅(a, b) F₃(a, b) an integer?The number obtained by taking the last two digits of 5²⁰²⁴ in the same order is:Find the largest positive integer n < 30 such that 1 2 (n^8+3 n^4-4 ) is not divisible by the square of any prime number.Let F_k(a, b)=(a+b)^k-a^k-b^k and let S= 1,2,3,4,5,6,7,8,9,10 . For how many ordered pairs (a, b) with a, b S and a b is F₅(a, b) F₃(a, b) an integer? Full Binomial Theorem list All Olympiad workbook PYQs