Recent content by danieldf

I don't know about the requirements of a statement to be considered an axiom, but as I see it, seems axioms are to be more fundamental truths (which we consider to be). RH is such a complex proposition it seems to be pushing too much to consider it a axiom. Though there are a number of things...

Is anybody familiar with any theory of integer cevians on equilateral triangles? More specificaly, I was trying to find something about the number of integer cevians that divide the side in integer parts. Like, the eq triangle of side 8 have cevian 7 dividing one side into 3+5. Only reference...

This formula does not give all possible triples. It gives all primitives and a bunch of the non primitives, right? If you add the multiples of those then you get all. But then they wouldn't be uniquely expressed (I guess..?). Would it be relevant to find a formula which generates them all with...

I mean a solutions in one variable. Like (2n, n²-1,n²+1) is a solutioin for x²+y²=z²

Sorry.. I didn't explain before.

a(3b+1)=c The solutions are obvious. I want to know if there is a solution a(n), b(n) (and so, c(n)) or at least a solution a(b). Can someone help with that..?

But.. We can say that -1 = e^i(pi+2kpi) , can't we..? So, i think that "problem" doesn't invalidate the identity. It's just that we are talking about complex numbers and extending functions can show us some "strange" things if we look at it like we look to the reals. Remember the famous sum...

It is an identity. The use of 'i' really not matter. It's just a constant. And it follows right from the Euler's Formula: e^ti = cos t + i sin t which follows from Taylor expansion for e, sin and cos. With t=pi you have e^(pi i) = -1, so ln(-1)/i=pi

Oh really.. Sorry, i just forgot that. They're integers (naturals in fact) And i mean irreducible over rationals. Thx!

The polynomial is x^n + A1x^(n-1) + A2x^(n-2) + ... + A2x^2 + A1x + 1. Where An (integer) is not zero for all n and n is even. For example: x²+x+1; x^4+2x^3+3x^2+2x+1. I'm looking for a method to say if that kind of polynomial is irreducible over racionals... Or when it is. Thx!