## Show that \$1^{1987} + 2^{1987} + \cdots + n^{1987}\$ never divides \$n+2\$

Show that for any natural number $$n$$, the result of $$1^{1987}+2^{1987} + \cdots + n^{1987}$$ cannot be divided by $$n+2$$ without a remainder.