Geodesic
Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$
Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 577-588.

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In this paper the special diophantine equation $\frac{q^{n}-1}{q-1}=y$ with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of $y-1$.
Classification : 11A41, 11D41, 11D45, 11D61, 11D72
Keywords: diophantine equation; Fermat and Mersenne primes; Catalan conjecture 
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     author = {Polick\'y, Zden\v{e}k},
     title = {Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {577--588},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2005},
     mrnumber = {2174534},
     zbl = {1121.11031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2005__46_3_a17/}
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Polický, Zdeněk. Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$. Commentationes Mathematicae Universitatis Carolinae, Tome 46 (2005) no. 3, pp. 577-588. http://geodesic.mathdoc.fr/item/CMUC_2005__46_3_a17/