Does `qfbsolve(,3)` misses solutions in p=5;so=qfbsolve(Qfb(p,p,p),3*p,3)?

I am experimenting with integer factorization described in [1]

Does qfbsolve(,3) misses the solution [1,1] in:

? p=5;so=qfbsolve(Qfb(p,p,p),3*p,3)
%5 = [[2, -1]]

[1]:  https://mathoverflow.net/questions/474328/could-efficient-solutions-of-x2n-y2-a-be-related-to-integer-factorization
Could efficient solutions of x^2+n y^2=A be related to integer factorization?