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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

Answer: A

\(\left (x^{n}-1 \right )\) 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 \(7+1\), \(8\)

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