Let $n > 1$ be an integer. Which of the following sets of numbers necessarily contains a multiple of $3$ ?

n^{19} - 1, n^{19} + 1

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n^{19}, n^{38} - 1

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n^{38}, n^{38} + 1

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n^{38}, n^{19} - 1

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Solution

The correct option is B $n^{19}, n^{38} - 1$
If $n = 3 m$ then $n^{19}$ is multiple of $3$
If $n = 3 m + 1$ or $3 m + 2$ then $n^{38} - 1$ is multiple of $3$ by binomial expansion

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Let n>1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?

The correct option is B n19,n38−1If n=3m then n19 is multiple of 3If n=3m+1 or 3m+2 then n38−1 is multiple of 3 by binomial expansion

Let $n > 1$ be an integer. Which of the following sets of numbers necessarily contains a multiple of $3$ ?

The correct option is B $n^{19}, n^{38} - 1$
If $n = 3 m$ then $n^{19}$ is multiple of $3$
If $n = 3 m + 1$ or $3 m + 2$ then $n^{38} - 1$ is multiple of $3$ by binomial expansion