Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 616.10003
Autor: Erdös, Paul; Pálfy, Péter Pál; Szegedy, M.
Title: a (mod p) \leq b (mod p) for all primes p implies a = b. (In English)
Source: Am. Math. Mon. 94, 169-170 (1987).
Review: The assertion of the title was conjectured by P.P.Pálfy, and P.Erdös pointed out that it easily follows from the Sylvester-Schur theorem. Then it was set as a problem in the Hungarian annual mathematics contest for college students. The most elegant solution was given by M.Szegedy, and that is what we present here. Theorem. Let a and b be positive integers. If, divided by any prime number, the residue of a is less than or equal to the residue of b, then a and b are equal.
Classif.: * 11A05 Multiplicative structure of the integers
11A07 Congruences, etc.
Keywords: divisibility by primes; Sylvester-Schur theorem
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