Bernadette Faye

activity

20152023

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Showing 2018Show all

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math.NT2018

An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers

Salah E. Rihane, Bernadette Faye, Florian Luca +1

In this paper, we find all solutions of the exponential Diophantine equation $B_{n + 1}^{x} - B_{n}^{x} = B_{m}$ in positive integer variables $(m, n, x)$ , where $B_{k}$ is the $k$ -th term of the…

math.NT2018

Fields generated by sums and products of singular moduli

Bernadette Faye, Antonin Riffaut

We show that the field $Q (x, y)$ , generated by two singular moduli~ $x$ and~ $y$ , is generated by their sum $x + y$ , unless~ $x$ and~ $y$ are conjugate over~ $Q$ , in wh…