# Abel-Runge lemma [closed]

I read recently that there exists an Abel-Runge lemma. What is it? Google does not give an answer. I know about Abel's lemma (the summation by parts) and the Runge-Kutta method but I have never heard about Abel-Runge lemma before.

Update. This is a history of mathematics question. Apparently there was a result of Abel which was later modified (generalized?) by Runge. I do not know the work of Runge well enough to find out what it was. Hence the question.

• Could you give a link or reference to the Russian text? It would help to know what the lemma states, or at least is about. It might be better known under a different name. Sep 26 at 9:06
• Is this the text? Judging by Google translation the author is just randomly putting some mathematical names into a playful verse, along with lots of other names. Sep 26 at 9:22
• @Conifold: As a Russian speaker, I do not need Google translate, and confirm your conclusion: this is not a mathematical text, and the author just plays with names. Sep 26 at 11:56
• "The translation from Russian is that there exist Dedekind calculations, an Abel-Runge lemma, Young modulus, etc. I am not sure it would help if I included that in the question." I think it might help to include a reference, as well as the relevant quotation and translation. Certainly, no harm can occur, at the very least. Sep 27 at 7:00
• @TheAmplitwist: Thank you for suggestion. Sep 27 at 7:12

I found two papers by Runge about solving polynomial equations (one published in 1885, Runge, C. On the solvable equations of the form $$x^5+ u x + v = 0$$ (German) Acta Math. 7 (1885), no. 1, 173-186, and one published in 1963, about 40 years after Runge's death, by Ostrovski, Runge, Carl Eine Vorzeichenregel in der Theorie der algebraischen Gleichungen. (German) Jber. Deutsch. Math.-Verein. 66 (1963/64), Abt. 1, 52–66). None of them mentions Abel. So I guess the Abel-Runge lemma does not exist and this answers my question.