A. Tall

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math.NT2023

The Diophantine equation $a (\frac{b ^{k} - 1}{b - 1}) = U_{n} - U_{m}$

P. Tiebekabe, I. Diouf, A. Tall +1

Here, we find all positive integer solutions of the Diophantine equation in the title, where $(U_{n})_{n ⩾ 0}$ is the generalized Lucas sequence $\mathcal{U}_0=0, \…

math.NT2022

The Scholz conjecture on addition chain is true for infinitely many integers with $ℓ (2 n) = ℓ (n)$

Amadou Tall

It is known that the Scholz conjecture on addition chains is true for all integers $n$ with $ℓ (2 n) = ℓ (n) + 1$ . There exists infinitely many integers with $\ell(2n) \leq \ell(n…

The Diophantine equation a(b−1bk−1​)=Un​−Um​

The Scholz conjecture on addition chain is true for infinitely many integers with ℓ(2n)=ℓ(n)

The Diophantine equation $a (\frac{b ^{k} - 1}{b - 1}) = U_{n} - U_{m}$

The Scholz conjecture on addition chain is true for infinitely many integers with $ℓ (2 n) = ℓ (n)$