Let us consider 2^{1987}+3^{1987}+\cdots+(n)^{1987}
We have k^{1987} + (n+2-k) ^{1987 } is divisible by n+ 2
If n is odd taking k from 2 to \frac{n-1}{2} we have |frac{n-1}{2}$ pairs and eac pair is divisible by n+2 and adding 1 does not divide by 1
If n is even taking k from 2 to \frac{n}{2} we have \frac{n}{2} pairs and each pair is divisible by n+2 and middle number is (\frac{n+2}{2})^{1987}
If n+ 2 is a multiple of 4 this is even and adding 1 makes it odd and hence the sum is not divisible by n+ 2
If n+2 is of the form 4m+ 2 and in this case divisible by 2m+ 1so adding 1 does not make it divisible by 2m+ 1 so not divisible by n+ 2 proved
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