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- W2950598286 abstract "We prove a result that finishes the study of primitive arithmetic progressions consisting of squares and fifth powers that was carried out by Hajdu and Tengely in a recent paper: The only arithmetic progression in coprime integers of the form (a^2, b^2, c^2, d^5) is (1, 1, 1, 1). For the proof, we first reduce the problem to that of determining the sets of rational points on three specific hyperelliptic curves of genus 4. A 2-cover descent computation shows that there are no rational points on two of these curves. We find generators for a subgroup of finite index of the Mordell-Weil group of the last curve. Applying Chabauty's method, we prove that the only rational points on this curve are the obvious ones." @default.
- W2950598286 created "2019-06-27" @default.
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- W2950598286 date "2009-12-14" @default.
- W2950598286 modified "2023-09-27" @default.
- W2950598286 title "On a problem of Hajdu and Tengely" @default.
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