On generalizations of a problem of Diophantus
Bugeaud, Yann ; Gyarmati, Katalin
Illinois J. Math., Tome 48 (2004) no. 3, p. 1105-1115 / Harvested from Project Euclid
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Let $k \ge 2$ be an integer and let ${\mc A}$ and ${\mc B}$ be two sets of integers. We give upper bounds for the number of perfect $k$-th powers of the form $ab+1$, with $a$ in ${\mc A}$ and $b$ in ${\mc B}$. We further investigate several related questions.
Publié le : 2004-10-15
Classification:  11D99,  11B75 
@article{1258138502,
     author = {Bugeaud, Yann and Gyarmati, Katalin},
     title = {On generalizations of a problem of Diophantus},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 1105-1115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138502}
}

Bugeaud, Yann; Gyarmati, Katalin. On generalizations of a problem of Diophantus. Illinois J. Math., Tome 48 (2004) no. 3, pp.  1105-1115. http://gdmltest.u-ga.fr/item/1258138502/