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Question 2
If x is the remainder when $$3^{61284}$$ is divided by 5 and y is the remainder when $$4^{96}$$ is divided by 6, then what is the value of (2x - y)?
Solution
x is the remainder when $$3^{61284}$$ is divided by 5
So, $$\frac{3^{61284}}{5}$$ = $$\frac{3^{4 \times 15321}}{5}$$
= $$\frac{3^{4}}{5}$$ = $$\frac{81}{5}$$
Remainder = 1
x = 1
y is the remainder when $$4^{96}$$ is divided by 6
So $$\frac{3^{96}}{6}$$ = $$\frac{3^{4 \times 24}}{5}$$
= $$\frac{4^{4}}{6}$$ = $$\frac{256}{6}$$
Remainder = 4
y = 4
Now,
(2x - y) = 2 - 4 = -2
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