A note on integral clock triangles.
A parametric family of elliptic curves
A parametric family of quartic Thue equations
A parametric family of sextic Thue equations
A remark on prime divisors of lengths of sides of Heron triangles.
A solution to an “unsolved problem in number theory”.
A symmetric diophantine system concerning fifth powers
Almost powers in the Lucas sequence
The famous problem of determining all perfect powers in the Fibonacci sequence and in the Lucas sequence has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations , with and , for all primes and indeed for all but primes . Here the strategy of [10] is not sufficient due to the sizes of...