## 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

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