$29 \cdot 55$ When $x^{13}+1$ is divided by $x-1$, the remainder is
(A) 1 .
(B) -1 .
(C) 0 .
(D) 2 .
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] When $x-a$ divides the integer-coefficient polynomial $f(x)$, the remainder is $f(a)$, so when $x^{13}+$ 1 is divided by $x-1$, the remainder is $1^{13}+1=2$.
Therefore, the answer is $(D)$.