The Terai-Jeśmanowicz conjecture on the equation \(a^x+b^y=c^z\) (Q2706879)

Let \(m\) be a positive integer with \(2\mid m\). In this paper the authors prove that if \((a,b,c)= (m^3-3m, 3m^2-1, m^2+1)\) or \((|m^5- 10m^3+ 5m|\), \(5m^4- 10m^2+1\), \(m^2+1)\), \(b\) is an odd prime, then the equation \(a^x+b^y=c^z\) has only the positive integer solution \((x,y,z)= (2,2,3)\) or \((2,2,5)\).NEWLINENEWLINENEWLINE\{Reviewer's remark: The Terai-Jeśmanowicz conjecture given in reference [3] is false\}.