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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 427.10004

**Autor: ** Erdös, Paul

**Title: ** How many pairs of products of consecutive integers have the same prime factors? (Research problem). (In English)

**Source: ** Am. Math. Mon. 87, 391-392 (1980).

**Review: ** The solution of the recurrence relation f_{n} = aF_{n-1}-bF_{n-2} is shown to be very simply connected to the number of distinct partitions of a segment of length n into p parts of length 2 and (n-2p) parts of length 1. A sum rule is obtained and known results concerning Fibonacci numbers (for which a = b = 1) are recovered.

**Classif.: ** * 11A41 Elemementary prime number theory

00A07 Problem books

**Keywords: ** pairs of products of consecutive integers; prime factors

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