On a generalized recurrence for Bell numbers.
For , let be fixed numbers of the set , and let
The number of solutions of the congruence in the box is estimated from below in the best possible way, provided for all i,j either or or .
We study a simultaneous diophantine problem related to Littlewood’s conjecture. Using known estimates for linear forms in -adic logarithms, we prove that a previous result, concerning the particular case of quadratic numbers, is close to be the best possible.