Abstract:

The problem of the solution number about m=(m₁,m₂,…,m_2r) was studied, when the congruence can be solved. By introducing the conception of the p-adic exponential evaluation and comparing the p-adic exponential evaluations of each coefficient of x in the congruence, we obtain the solution number of m in the congruence when r=6.

Key words: congruence; number of solutions; p-adic exponential evaluation; character sum