Question Number 30588 by abdo imad last updated on 23/Feb/18
![(n_k )_(1≤k≤n) is a family of integrs numbers let put p(x)=Σ_(k=1) ^n x^n_k and q(x)= Σ_(j=0) ^(n−1) x^j if n_k ≡k−1[n] prove that q divide p.](https://www.tinkutara.com/question/Q30588.png)
$$\left({n}_{{k}} \right)_{\mathrm{1}\leqslant{k}\leqslant{n}} \:{is}\:{a}\:{family}\:{of}\:{integrs}\:{numbers}\:{let}\:{put} \\ $$$${p}\left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:{x}^{{n}_{{k}} } \:\:\:{and}\:{q}\left({x}\right)=\:\sum_{{j}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{x}^{{j}} \: \\ $$$${if}\:{n}_{{k}} \equiv{k}−\mathrm{1}\left[{n}\right]\:{prove}\:{that}\:{q}\:{divide}\:{p}. \\ $$