Abstract
AbstractLetpbe a prime and letr,sbe positive integers. In this paper, we prove that the Goormaghtigh equation$(x^m-1)/(x-1)=(y^n-1)/(y-1)$,$x,y,m,n \in {\mathbb {N}}$,$\min \{x,y\}>1$,$\min \{m,n\}>2$with$(x,y)=(p^r,p^s+1)$has only one solution$(x,y,m,n)=(2,5,5,3)$. This result is related to the existence of some partial difference sets in combinatorics.
Publisher
Cambridge University Press (CUP)
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