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

Find all function `f(x)` if `(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^2-y^2)`

 Find all function `f(x)` if `(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^2-y^2)`

Solution