# Did Euler Know Quadratic Reciprocity?: New Insights from a Forgotten Work - Conclusion - Appendix

Author(s):
Paul Bialek (Trinity International University) and Dominic W. Klyve (Central Washington University)

### Conclusion

A careful reading of Euler's De divisoribus numerorum in forma $mxx + nyy$ contentorum (On divisors of numbers contained in the form $mxx + nyy$) (E744), then, shows that he did not make much progress along Edwards' ladder of theorems.  A statement of Lemma 5.1 does appear (in this more general setting) in Section 4 of the paper; nothing else indicates that Euler had any notion of reciprocity.  While we continue to be impressed with E744, we cannot from this work see any further evidence that Euler had an inkling of quadratic reciprocity in the sense in which we usually understand it.  The credit for this theorem must continue to rest with Euler's intellectual heirs, Legendre and Gauss.

### Appendix

Editor's note: The authors have translated Euler's De divisoribus numerorum in forma $mxx + nyy$ contentorum (E744) from Latin into English.  Read their translation of Euler's E744, On divisors of numbers contained in the form $mxx + nyy.$