Resumen de Regular solutions of a congruence system

Catalina Calderón García , M. J. de Velasco

• In this paper we give bounds and recurrence formulae for the number of solutions of the system $\sum^k_{t=1}x^v_t\equiv\lambda_v(\mbox{mod }q_v), 1\leq v\leq n, \quad\lambda_v, q_v\in\mathbb{N}$ which satisfy the conditions $\gamma_i x_i\equiv\beta_i(\mbox{mod } q), g.c.d.(\gamma_i,q)= d_i\vert\beta_i$ and $q= l.c.m.(q_1,\dots,q_n)$ where $\gamma_i, \beta_i$ and $q$ are given integers.