Question 53

What is the remainder when we divide $$5^{70} - 7^{70}$$ by 24 ?

Solution

When $$5^{70} + 7^{70}$$ is divide by 24,

$$\frac{5^{70} + 7^{70}}{24}$$

= $$\frac{(5^2)^{35} + (7^2)^{35}}{24}$$ = $$\frac{25^{35} + 49^{35}}{24}$$

= $$\frac{25^{35}}{24}+ \frac{49^{35}}{24}$$

Remainder = $$(1)^{35} - (1)^{35}$$ = 1 - 1 = 0

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