Yes. You can try the following smt2 script with yices2 [0]:
(set-logic QF_UFNIA)
(declare-fun x () Int)
(declare-fun y () Int)
(declare-fun z () Int)
(define-fun left-side () Int
(+ (+
(* (* x (+ x z)) (+ x y))
(* (* y (+ y z)) (+ x y)))
(* (* z (+ y z)) (+ x z)))
)
(define-fun right-side () Int
(* (* (*
4
(+ y z))
(+ x z))
(+ x y))
)
; disallow division by zero
(assert (not (= 0 (+ y z))))
(assert (not (= 0 (+ x z))))
(assert (not (= 0 (+ x y))))
(assert (= left-side right-side))
(check-sat)
(get-model)
Anything is possible, but I really doubt you'll find those 80 digit numbers. Maybe the sat solver includes some serious number theory though. I doubt it.
Does the `Int` datatype allow negative integers or is it non-negative only? This problem gets much more difficult if you restrict it to positive solutions only.
[0]: http://yices.csl.sri.com/