/sci/ - Science & Math

Hello, I'm the guy who had recently proven Dirichlet's theorem (nobody cares for some reason) even though one could have stolen the idea right away but everybody is worthless so I will be the one to steal my own idea (hurray!)

I'm currently finishing (maybe) writing a paper regarding some conjectures on primes and have came up with one interesting yet maybe easy conjecture.

It simply states that all prime chains are finite.

Where one defines prime [math] f [/math]-chains as a "tuple" or a sequence of prime elements [math] p=(p_1, \dots, p_n) [/math] over a GCD domain with infinitely many prime elements [math] K [/math] equipped with an irreducible polynomial [math] f\in K[x] [/math] so that the sequence [math] p [/math] is an indexed iteration of [math] f [/math] on [math]p_1[/math] meaning that [math] p_i=f^{i-1}(p_1),\; i=1, \dots, n [/math]

More intuitive and weaker conjecture would be that all prime [math] f [/math]-chains are finite for any irreducible polynomials [math]f\in\mathbb{Z}[x][/math]

Can you prove this conjecture true? Or maybe false.

In any case an even weaker case has been proven by Günter Löh regarding Cunningham chains stating that all of them are finite.

One may actually use Lagrange's theorem in order to prove that all Generalized Cunningham chains are finite, can you figure out why?

Good luck!

I have to disapprove that a thrivariate function
[eqn]q(n, a, b)=n(a^2+b^2)-b[/eqn] with [math]q:\mathbb{N}^3\rightarrow\mathbb{N}[/math] is a surjection

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