Squares in arithmetic progression over number fields
classification
🧮 math.AG
math.NT
keywords
numberarithmeticboundfieldfieldsprogressionsquaresdegree
read the original abstract
We show that there exists an upper bound for the number of squares in arithmetic progression over a number field that depends only on the degree of the field. We show that this bound is 5 for quadratic fields, and also that the result generalizes to $k$-powers for $k>1$.
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