Question

${18}^n-2^{4n}$ is divisible by $34$.

• A. All values of $n$
• B. Even values of $n$
• C. Odd values of $n$
• D. No value

Answer 1

Answer: (B)

Even values of $n$

${18}^n-2^{4n}$ can be written as ${18}^n-{16}^n$

${18}^n$ $-$ ${16}^n$ is divisible by $18+16=34$ for even values.

As $a^n$-$b^n$ is divisible by $a+b$ only for even values of $n$.