Question 47
For a positive integer $n$ we define $D_{n}$ as the largest number that is a divisor of $a^{n}+(a+1)^{n}+(a+2)^{n}$ for all positive integers $a$.
a. Prove that for every positive integer $n$ the number $D_{n}$ is of the form $3^{k}$ with $k \geq 0$.
b. Prove that for every $k \geq 0$ there exists a positive integer $n$ such that $D_{n}=3^{k}$.
a. Prove that for every positive integer $n$ the number $D_{n}$ is of the form $3^{k}$ with $k \geq 0$.
b. Prove that for every $k \geq 0$ there exists a positive integer $n$ such that $D_{n}=3^{k}$.