Recent content by Feryll

Thanks, you really cleared up some concepts, then. Also, yes, I must have meant quotient. Not sure where the sub came from.

This has to do with number theory along with group and set theory, but the main focus of the proof is number theory, so forgive me if I'm in the wrong place. I've been struggling to understand a piece of a proof put forth in my book. I know what the Gaussian integers are exactly, and what a...

I'm don't think that you meant this, but it should be reiterated that one does not ever need to find a factor of a number to prove that it's composite, even for extraordinarily large numbers.

Well, we know it has no solutions x>1 (There's a special case x=0, d=1, and y=-1, though) when d is a cubed integer, as then d^3*y^3 would also be a cubed integer. And since there is no difference between two cubed integers that is only 1 (they grow further and further apart from each other)...

Yep, that's it. (One of the things that depresses me about these problems is the difficulty in calculation; as you can see, we would have to evaluate all of the terms to over 40,000 just to calculate T(8); if someone could guide me to a simple algorithm to calculate the elements with a computer...

EDIT: I just noticed something on reflection that, being me, I got wrong in the OP. If you end up with two or more repeats of output elements when figuring out the factorizations' greatest factors, you must repeat it that many times, which I didn't really specify. See below for implciations...

Certain and Curious Number Sequence (w/ primes) This is the number sequence a(x) whose output is determined by the greatest integer divisor n of any factorization of a with the additional rule that if an element is repeated in the factorization, the factorization must be thrown out. EX: a(56)...