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Offprint first edition. Presentation copy, inscribed by the author. Text in German. Papered spine. pp. [193]-198. Inscribed offprint of ErdÅ s' first publication, a proof of the Bertrand-Chebyshev theorem. ErdÅ s' first paper, written at age 19 as a freshman at the university in Budapest, a major contribution to number theory, a proof of the Bertrand-Chebyshev theorem, using basic properties of binomial coefficients. "ErdÅ s's proof stunned the international mathematical community with its brevity and elegance. It gave [the] world its first taste of a proof style that was to become indelibly associated with Paul ErdÅ s" (Hill, 2004). Originally published in Acta Litterarum ac Scientiarum [.] [Acta Litt. Sci. Szeged 5 (1932)], exceedingly scarce as an offprint, we could not trace any copies in institutional holdings worldwide. Zbl. 4,101; Grossman 1932.01 Literature: Grossman, J.: List of Publication of Paul ErdÅ s, September 2010. Hill, J. (2004, 4 June): Paul ErdÅ s: Mathematical Genius, Human (In That Order). ErdÅ s, Pál [Paul]: Egy Kürschák-féle elemi számelméleti tétel általánosítása. [Generalization of an Elementary Number-Theoretic Theorem of Kürschák.] (Sonderabdruck aus "Matematikai és Fizikai Lapok" Band XXXIX. Budapest 1932. / Különlenyomat a "Matematikai és Fizikai Lapok"XXXIX. kötetébÅ l. Budapest 1932.) [Budapest]: [Matematikai és Fizikai Lapok. XXXIX.],[1932]. pp. [17]-24. Offprint first edition. Text in Hungarian with a German abstract. Papered spine. Pages yellowed due to aging, otherwise in fine condition. Offprint edition of ErdÅ s' second publication, dealing with the Egyptian fraction. ErdÅ s' second paper, written at age 19 as a freshman at the university in Budapest, in which he generalizes an elementary result of József Kürschak (A harmonikus sorról [On Harmonic Progression], 1918), and proves that the sum of the reciprocals of any number of equally spaced integers is never a reciprocal. Originally published in Matematikai és Fizikai Lapok [Mat. Fiz. Lapok 39 (1932)], exceedingly scarce as an offprint, we could not trace any copies in institutional holdings worldwide. Zentralblatt 7,103; Grossman 1932.01 Literature: Grossman, J.: List of Publication of Paul ErdÅ s, September 2010. ; Weisstein, E. W.: Egyptian Fraction. From MathWorld - A Wolfram Web Resource, Retreived from ErdÅ s, Paul: A Theorem of Sylvester and Schur. (Extracted from the Journal of the London Mathematical Society, Vol. 9, Part 4.) [London]: [Journal of the London Mathematical Society(Printed by C. F. Hodgson & Son)], [1934]. pp. [282]-288 [1]. Offprint first edition. Text in English. In publisher's green printed wrappers. In fine condition. Offprint of ErdÅ s' first papers in English, written in 1934, soon after his arrival to England for a postdoctoral fellowship at Manchester. Scarce as an offprint, WorldCat locates no copies of such edition in institutional holdings. Zbl. 10,103; Grossman 1934.01 ErdÅ s, Paul; Turán, Paul: On a Problem in the Elementary Theory of Numbers. (Reprinted from the American Mathematical Monthly. Vol. XLI, No. 10 December, 1934.) USA: American Mathematical Monthly, 1934. pp. [1] [608]-611 [1]. Offprint first edition. In publisher's gray printed wrappers. In fine condition. ErdÅ s' first American publication, also the first co-authored with Paul Turán. Offprint of ErdÅ s' early paper co-authored with Paul Turán, written in 1934. The two had a long collaboration, lasting 46 years and resulting in 28 joint papers. Scarce as an offprint, WorldCat locates no copies of such edition in institutional holdings. Zbl. 10,294; Grossman 1934.03 ErdÅ s, Paul: On the Density of the Abundant Numbers. (Extracted from the Journal of the London Mathematical Society, Vol.9, Part 4.) [London]: [Journal of the London Mathematical Society (Printed by C. F. Hodgson & Son)], [1934]. pp. [278]-282 [1]. Offprint first edition. Text in English. Papered spine. In fine condition. Offprint of one of the earliest papers of ErdÅ s in Engl. Seller Inventory # 2039
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