What is the remainder when $25 * (1331)^{2196}$ is divided by 13?

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Official Explanation

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We need to find the remainder when

25 * (1331)^{2196}

is divided by 13.

- 25 divided by 13 gives a remainder of

25 - 13 = 12

, which is equivalent to

-1

modulo 13.

- 1331 divided by 13:

1331 \div 13 = 102

remainder

5

, so 1331 ≡ 5 (mod 13).

Thus the expression becomes:

(-1) \times (5)^{2196} \mod 13

.…

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.