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Pythagorean primes and palindromic continued fractions. (English) Zbl 1134.11322
Summary: In this note, we prove that every prime of the form \(4m+1\) is the sum of the squares of two positive integers in a unique way. Our proof is based on elementary combinatorial properties of continued fractions. It uses an idea by H. J. S. Smith [J. Reine Angew. Math. 50, 91–92 (1855; ERAM 050.1326cj)]. Smith’s proof makes heavy use of nontrivial properties of determinants. Our purely combinatorial proof is self-contained and elementary.

MSC:
11D85 Representation problems
11A55 Continued fractions
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