1950 AHSME Problems/Problem 20

Problem

When $x^{13}+1$ is divided by $x-1$ , the remainder is:

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ -1\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \text{None of these answers}$

Use synthetic division, and get that the remainder is $\boxed{\mathrm{(D)}\ 2.}$

By the remainder theorem, the remainder is equal to the expression $x^{13}+1$ when $x=1.$ This gives the answer of $\boxed{\textbf{(D)}\ 2.}$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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