求所有自然數n使26.5^n+37.5^n為正整數?

1. As n=2m, even integer => non integer because of the second term [...];
2. As n=2m+1,odd integer: 1,3,5,7 => integer because [...]=0 and terms in summation are all integers;
3. As n is odd but beyond 7, the term in summation generated by small k may bring non-integer terms. e.g. k=1 for n=9. Thus the whole sum still fails to be an integer.