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For what it's worth: Concrete Mathematics does have an attribution to Kummer — it's just that the credits are given separately in Appendix C, "Credits for Exerc
by svat 1y ago
For what it's worth: Concrete Mathematics does have an attribution to Kummer — it's just that the credits are given separately in Appendix C, "Credits for Exercises", where on page 634, next to 5.36 (the exercise number you mentioned), you can find "Kummer [230, p. 116]" and [230] (on page 621, in Appendix B, "Bibliography") gives the full citation:
> E. E. Kummer, “Über die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen,” Journal für die reine und angewandte Mathematik 44 (1852), 93–146. Reprinted in his Collected Papers, volume 1, 485–538.
Also, the answer to exercise 5.36 says “See [226] for extensions of this result
to generalized binomial coefficients” and [226] (on page 620) is:
> Donald E. Knuth and Herbert S. Wilf, “The power of a prime that divides a generalized binomial coefficient,” Journal für die reine und angewandte Mathematik 396 (1989), 212–219
which of course begins (https://www2.math.upenn.edu/~wilf/website/dm36.pdf https://www2.math.upenn.edu/~wilf/website/dm36.pdf) by citing Kummer. (Looks like the authors published in the same journal as Kummer, 137 years later!)
- gjm11 1y agoOh, good catch! I hadn't noticed they had a separate credits-for-exercises section. I did notice that ex 5.36 references a paper of Knuth & Wilf, but references aren't transitive :-).
- coderatlarge 1y agothank you for your help in tracking this down! i will check it out…