NDA2025MathematicsBinomial TheoremActual

What is the remainder when 5⁹⁹ is divided by 13 ?

Options

Correct answer

C. 8

Step-by-step solution

To find the remainder when 5⁹⁹ is divided by 13 , we evaluate the powers of 5 modulo 13 . 5^1 5 13 5^2 = 25 -1 13 Squaring both sides gives: 5^4 (-1)^2 1 13 We can express 5⁹⁹ in terms of 5^4 as follows: 5⁹⁹ = 5⁹⁶ 5^3 = (5^4)²⁴ 125 Substituting 5^4 1 13 : 5⁹⁹ (1)²⁴ 125 13 5⁹⁹ 125 13 Dividing 125 by 13 yields 125 = 13 9 + 8 . Thus, 125 8 13 . The remainder is 8 . Answer: 8

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