## 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