#### Glasnik Matematicki, Vol. 42, No.2 (2007), 273-279.

### ON POWERS IN SHIFTED PRODUCTS

### K. Gyarmati and C. L. Stewart

Alfréd Rényi Institute of Mathematics, 13-15 Reáltanoda u.,
1053 Budapest, Hungary

*e-mail:* `gykati@renyi.hu`
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

*e-mail:* `cstewart@uwaterloo.ca`

**Abstract.** In this note we give an estimate for the size of a subset
*A* of {1, ..., *N*} which has the property that
the product of any two distinct elements of *A* plus 1 is a perfect power.

**2000 Mathematics Subject Classification.**
11B75, 11D99.

**Key words and phrases.** Perfect powers, extremal graph theory.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.42.2.02

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