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Discussion

x divides $$\left ( \left ( 49 \right )^{15} -1\right )$$ completely. What is $$x$$ ?

• A.8
• B.14
• C.50
• D.51

$$\left (x^{n}-1 \right )$$ is divisible by $$x+1$$ if $$x$$ is an even number.
$$\left ( \left ( 49 \right )^{15} -1\right )$$  =$$\left ( \left ( 7^{2} \right )^{15} -1\right )$$  =$$\left ( 7 \right )^{30} -1$$
which is divisible by $$7+1$$, $$8$$