A generalization of Gauss' triangular theorem

Jangwon Ju, Byeong-Kweon Oh

A quadratic polynomial ${\Phi }_{a,b,c}(x,y,z)=x(ax+1)+y(by+1)+z(cz+1)$ is called universal if the diophantine equation ${\Phi }_{a,b,c}(x,y,z)=n$ has an integer solution $x,y,z$ for any non n…