Prove that the polynomial \[ x^{9999}+x^{8888}+x^{7777}+\cdots+x^{1111}+1 \] is divisible by \[ x^9+x^8+x^7+\cdots+x+1 \]

 Problem: 01

Prove that the polynomial `x^9999+x^8888+x^7777+...+x^1111+1` is divisible by `x^9+x^8+x^7+....+x+1`

Solution