Sums of Three Squares in Function Fields of Conics and Cassels–catalan Curves
نویسنده
چکیده
We show that a function field in one variable of genus zero has pythagoras number two if and only if either the base field is hereditarily pythagorean and, in case the function field is nonreal, uniquely ordered, or −1 is a square in the base field. We generalize one implication to function fields of Cassels-Catalan curves.
منابع مشابه
Perfect Powers That Are Sums of Consecutive Cubes
Euler noted the relation 63= 33+43+53 and asked for other instances of cubes that are sums of consecutive cubes. Similar problems have been studied by Cunningham, Catalan, Gennochi, Lucas, Pagliani, Cassels, Uchiyama, Stroeker and Zhongfeng Zhang. In particular, Stroeker determined all squares that can be written as a sum of at most 50 consecutive cubes. We generalize Stroeker’s work by determi...
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