Zden\v ek Polick\'y

Zden\v ek Polick\'y
Diophantine equation $\frac {q^{n}-1}{q-1}=y$ for four prime divisors of $y-1$

Comment.Math.Univ.Carolinae 46,3 (2005) 577-588.

Abstract: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 $y-1$.

Keywords: diophantine equation, Fermat and Mersenne primes, Catalan conjecture
AMS Subject Classification: Primary 11D72; Secondary 11D45

PDF

Zden\v ek Polick\'y Diophantine equation $\frac {q^{n}-1}{q-1}=y$ for four prime divisors of $y-1$

Zden\v ek Polick\'y
Diophantine equation $\frac {q^{n}-1}{q-1}=y$ for four prime divisors of $y-1$