Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mo...Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mod n in(Z/nZ)^(2) such that xi∈(Z/nZ)^(×)for i∈J⊆{1,2}.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11571328).
文摘Given a binary quadratic polynomial f(x_(1),x_(2))=αx_(1)^(2)+βx_(1)x_(2)+γx_(2)^(2)∈Z[x_(1),x_(2)],for every c∈Z and n≥2,we study the number of solutions NJ(f;c,n)of the congruence equation f(x_(1),x_(2))≡c mod n in(Z/nZ)^(2) such that xi∈(Z/nZ)^(×)for i∈J⊆{1,2}.
