Question 115
A natural number $d$ is called *nice* if, for every pair of integers $(x, y)$,
$$
d\left|(x+y)^{5}-x^{5}-y^{5} \Longleftrightarrow d\right|(x+y)^{7}-x^{7}-y^{7}
$$
Show that there are infinitely many nice numbers. Are 2017 and 2018 nice?
$$
d\left|(x+y)^{5}-x^{5}-y^{5} \Longleftrightarrow d\right|(x+y)^{7}-x^{7}-y^{7}
$$
Show that there are infinitely many nice numbers. Are 2017 and 2018 nice?