Thread: for PH and others so inclined

"Show that

is always an integer for integral values of x".

It is relatively easy (but messy) to show that for each positive integer N
is a multiple of 15.
an other

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:



and



Therefore, it's an integer.

Seems rather logical. But, I am not that much of a number theorist. Have been learning it, though.

Originally Posted by Plato

It is relatively easy (but messy) to show that for each positive integer N
is a multiple of 15.
an other

Hello Plato,

use mathematical induction to prove this property:

Prove that













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

EB

Merry Christmas and a happy New Year.