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The Extended Generating Function of the Radical of n and the abc-Conjecture
Constantin M. Petridi
An extended generating series of the radical of n, involving two variables, leads to an identity in said variables, which proves Bombieri's abc-Conjecture for certain sets of integ…
The Sums of the powers of the Euler set and their connection with Artin's conjecture for primitive roots
Constantin M. Petridi
We examine the sums of the th powers of the integers less than and prime to (Euler set) and prove a formula (new) for …
Finiteness properties of abc-equations c = a+b
Constantin M. Petridi
We classify integer abc-equations c = a + b (to be defined), according to their radical R(abc) and prove that the resulting equivalence classes contain only a finite number of such…
The integer recurrence P(n)=a+P(n-phi(a)) I
Constantin M. Petridi
We prove that for a positive integer a the integer sequence P(n) satisfying for all n, -infty<n<infty, the recurrence P(n)=a+P(n-phi(a)), phi(a) the Euler function, generates in in…
The number of abc-equations c^n=a+b stisfying the strong abc-conjecture
Constantine M. Petridi
We prove that the frequency of abc equations c^n = a+b satisfying the strong abc - conjecture is phi(c^n)/2+o(phi(c^n)/2), for n going to infinity.
The number of equations c=a+b satisfying the abc-conjecture
Constantin M. Petridi
We prove that for a positive integer and any given , , the number of equations , , with positive coprime integers and ,…