Question Number 168042 by cortano1 last updated on 01/Apr/22
$$\:\:{The}\:{number}\:{of}\:{natural}\:{number}\:{k} \\ $$$$\:{such}\:{that}\:{k}\mid\:{n}^{\mathrm{7}} −{n}\:{for}\:\forall{n}\:{natural} \\ $$$$\:{numbers} \\ $$
Commented by Rasheed.Sindhi last updated on 02/Apr/22
$$\mathcal{D}{epends}\:{upon}\:{individual}\:{n}. \\ $$
Answered by alephzero last updated on 02/Apr/22
$${n}^{\mathrm{7}} \:{is}\:{odd}\:{if}\:{n}\:{is}\:{odd}\:{and}\:{even}\:{if} \\ $$$${n}\:{is}\:{even} \\ $$$$\Rightarrow\:{n}^{\mathrm{7}} −{n}\:{is}\:{always}\:{even} \\ $$$$\Rightarrow\:{k}\:=\:\mathrm{2}\:\wedge\:{k}\:=\:\mathrm{1} \\ $$