"Show that

is always an integer for integral values of x".

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- December 22nd 2006, 02:07 PMgalactusfor PH and others so inclined
"Show that

is always an integer for integral values of x". - December 22nd 2006, 02:22 PMPlato
It is relatively easy (but messy) to show that for each positive integer N

is a multiple of 15.

an other - December 22nd 2006, 02:43 PMgalactus
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. - December 23rd 2006, 12:54 AMearboth
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.