R. Scott

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math.NT2011

The generalized Pillai equation $\pm r a^{x} \pm s b^{y} = c$

Reese Scott, Robert Styer

In this paper we consider $N$ , the number of solutions $(x, y, u, v)$ to the equation $(- 1)^{u} r a^{x} + (- 1)^{v} s b^{y} = c$ in nonnegative integers $x, y$ and integers $u, v \in {0, 1}$ …

math.NT2011

The generalized Pillai equation $\pm r a^{x} \pm s b^{y} = c$ , II

Reese Scott, Robert Styer

We consider $N$ , the number of solutions $(x, y, u, v)$ to the equation $(- 1)^{u} r a^{x} + (- 1)^{v} s b^{y} = c$ in nonnegative integers $x, y$ and integers $u, v \in {0, 1}$ , for given i…

math.NT2006

Comments on Le Maohua's 1999 paper in the Proc. Japan Acad

Reese Scott

Considering the equation $a^{x} + b^{y} = c^{z},$ Le gives an upper bound on the number of solutions $(x, y, z)$ , and a bound on $z$ . Here we give slight improvements to these results, als…

The generalized Pillai equation ±rax±sby=c

The generalized Pillai equation ±rax±sby=c, II

Comments on Le Maohua's 1999 paper in the Proc. Japan Acad

The generalized Pillai equation $\pm r a^{x} \pm s b^{y} = c$

The generalized Pillai equation $\pm r a^{x} \pm s b^{y} = c$ , II