On the Diophantine equation (xk-1) = (zk-1)
Bugeaud, Yann
HAL, hal-00085718 / Harvested from HAL
Text on HAL
Let k ≥ 3 be an integer. We study the possible existence of pairs of distinct positive integers (a, b) such that any of the three numbers a + 1, b + 1, and ab + 1 is a k-th power. We further investigate several related questions.
Publié le : 2004-07-05
Classification:  11D61,  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 
@article{hal-00085718,
     author = {Bugeaud, Yann},
     title = {On the Diophantine equation (xk-1) = (zk-1)},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00085718}
}

Bugeaud, Yann. On the Diophantine equation (xk-1) = (zk-1). HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00085718/