It is relatively easy (but messy) to show that for each positive integer N
is a multiple of 15.
That was a fast response, Plato . I noticed, since the semesters have come to a close, there hasn't been much posting.
Anyway, maybe I am off base, but
Now, use Fermat's theorem:
Therefore, it's an integer.
Seems rather logical. But, I am not that much of a number theorist. Have been learning it, though.
use mathematical induction to prove this property:
The 1rst summand is a multiple of 15 according assumption, the 2nd summand is a multiple of 15 because it contains the factor 15 and the last 3 summands add up to 15. Thus is multiple of 15 and therefore the asumption is true for all
Merry Christmas and a happy New Year.