#### Glasnik Matematicki, Vol. 40, No.1 (2005), 13-20.

### ON SHIFTED PRODUCTS WHICH ARE POWERS

### Florian Luca

Instituto de Matematicas, Universidad Nacional Autonoma de
Mexico, C.P. 58180, Morelia, Michoacan, Mexico

*e-mail:* `fluca@matmor.unam.mx`

**Abstract.** In this note, we improve upon results
of Bugeaud, Gyarmati, Sarkozy and Stewart concerning the size of a
subset *A* of {1,...,*N*} such
that the product of any two distinct elements
of *A* plus 1 is a perfect power. We also show that the
cardinality of such a set is uniformly bounded assuming the
*ABC*-conjecture, thus improving upon a result of
Dietmann, Elsholtz, Gyarmati and Simonovits.

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

**Key words and phrases.** Shifted products, perfect powers.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.1.02

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