The Scott-Styer conjecture on at most one solution to a^x + b^y = c^z is confirmed for c=7,13,97 and primes c of form 2^r*3+1 except finitely many effectively determinable cases.
Nagell,Des équations indéterminéesx 2 +x+ 1 =y n etx 2 +x+ 1 = 3y n (in Norwegian), Norsk Mat
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Handling some Diophantine equation via Euclidean algorithm and its application to purely exponential equations
The Scott-Styer conjecture on at most one solution to a^x + b^y = c^z is confirmed for c=7,13,97 and primes c of form 2^r*3+1 except finitely many effectively determinable cases.