Question 19

Find the remainder when $$(12^{13} + 12)$$ is divisible by $$13$$.

Solution

$$(12^{13} + 12)\div13$$

We can write this as

$$\frac{12^{13}}{13}$$ + $$\frac{12}{13}$$

Negative remainder for $$\frac{12^{13}}{13}$$ = $$-1^{13}$$ = -1

Negative remainder for $$\frac{12}{13}$$ = -1

So, -1 + -1 = -2

Therefore, required remainder = 13 - 2 = 11

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