T prove that a statement holds for any integer

Question

Prove that $$\frac{1}{5}n^5+\frac{1}{3}n^3+\frac{7}{15}n$$ is an integer for every integer $n$

I have no idea which concept to use here

Answer 1

You can prove by hypothesis we assume the given equation produces a natural number by substituting 1,2 which gives natural number hence we hypothesis it gives a natural number for n and the it is considered a natural number let say x and now we substitute n with (n+1) and prove it is a natural number I have done the proof if you try you Will get same you have to be familiar with (n+1)^5 who's cofficents are (1,5,10,10,5,1)