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Note on Products of Consecutive Integers
Author(s) -
Erdös P.
Publication year - 1939
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-14.3.194
Subject(s) - citation , information retrieval , computer science , combinatorics , library science , mathematics
of E consecut,ive positive integers is never an Z-th power, if k > 1 and 1 > 1. This is well known for k = 2 and Ic = 3, and was recently proved by G. Szekerest for k < 9. It has also been proved by Narumi$ for I = 2 and k < 202. In t,his note we prove the conjecture for I= 2 and all k ; that is, we prove that a product of consecutiveintegers is never a. square. The method is similar to that used by Narumi. Suppose that