Question 23
For every positive integer $n$, let $D_n$ be the greatest common divisor of all numbers of the form $a^n+(a+1)^n+(a+2)^n$, as $a$ ranges over the positive integers.
a. Prove that for every $n$, $D_n=3^k$ for some integer $k\ge0$.
b. Prove that for every $k\ge0$, there is an integer $n$ such that $D_n=3^k$.
a. Prove that for every $n$, $D_n=3^k$ for some integer $k\ge0$.
b. Prove that for every $k\ge0$, there is an integer $n$ such that $D_n=3^k$.