Regularity of Diophantine quadruples over $\mathbb{Q}(i)[X]$

Sanda Bujačić Babić, Ana Jurasić

We prove that every Diophantine quadruple $\{a,b,c,d\}$ over $\mathbb{Q}(i)[X]$ that contains at least one non-constant polynomial is regular; that is, $$(a+b-c-d)^2=4(ab+1)(cd+1).…