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• W2129322133 abstract "Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite order on the elliptic curve . Heegner constructed such rational points in the case that m are primes congruent to 5,7 modulo 8 or twice primes congruent to 3 modulo 8 [Monsky P (1990) Math Z 204:45–68]. We extend Heegner's result to integers m with many prime divisors and give a sketch in this report. The full details of all the proofs will be given in ref. 1 [Tian Y (2012) Congruent Numbers and Heegner Points, arXiv:1210.8231]." @default.
• W2129322133 created "2016-06-24" @default.
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• W2129322133 date "2012-12-04" @default.
• W2129322133 modified "2023-10-16" @default.
• W2129322133 title "Congruent numbers with many prime factors" @default.
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• W2129322133 doi "https://doi.org/10.1073/pnas.1216991109" @default.
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