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Remarks and results on congruent numbers. (English) Zbl 0259.10010

Proc. 3rd Southeast. Conf. Combinat., Graph Theory, Computing, Florida Atlantic Univ., Boca Raton 1972, 27-35 (1972).
A congruent number is a positive integer \(a\) such that the equations \(x^2+ay^2=z^2\) and \(x^2-ay^2=t^2\) are simultaneously soluble in positive integers \(x,y,z,t\). The authors have investigated the 608 square-free \(a\leq 1000\) with the help of a computer, whereby 198 of these numbers have been proved congruent and 136 non-congruent, the other 274 remain undecided. The results agree with the conjecture that every \(a\equiv 5,6\) or \(7\pmod 8\) is a congruent number.
For the entire collection see Zbl 0258.00003.
Reviewer: G. L. Watson

MSC:

11D09 Quadratic and bilinear Diophantine equations
11-04 Software, source code, etc. for problems pertaining to number theory

Citations:

Zbl 0258.00003