一类同余方程解数的上界估计

The Estimation of an Upper Bound for the Number of Solutions of a Kind of Congruences

主要研究形如的同余方程关于m=(m_1,…,m_(2r))解数估计问题,并得出当r=4,5时,该同余方程解数的上界估计.前者可改进Dodd的结论,而后者则可应用于对另一类同余方程组解数的上界估计.

This paper investigates the estimation of the solution number about m =（m1,……,m2r）of the congruences such as ^rЛi=1（X＋mi）≡^2rЛj=r＋1（X＋mj）（mod p^μ）,and gets the upper bound of the solution number of such congruence when r=4 and 5. The former result improves the Dodd＇s conclusion, and the latter can be used to estimate the solution number of the other kinds of congruences.