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Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Binomial Theorem

Olympiad workbook · IOQM · Binomial Theorem

The number obtained by taking the last two digits of 5^ 2024 in the...

The number obtained by taking the last two digits of

5^{2024}

in the same order is:

Correct answer

25

Step-by-step solution

Last two digits of

5^{2024}

\begin{aligned} \Rightarrow \quad & 5^{2024} \equiv a(\bmod 100) \\ & 5^4 \equiv 25(\bmod 100) \\ & 5^{2024} \equiv 25(\bmod 100) \end{aligned}

\Rightarrow \quad

last 2 digits in same order is 25

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