Thanks for the detailed response!  I ended up doing a numerical answer, asked for m then n in two different questions, and provided bounds on m and n so that each answer is unique. Reading your answer...

In a quiz about gcd, I'd like the students to come up with the factors in Bezout's identity. Namely, for a and b in N, there exist n and m in Z such that an + bm = gcd(a,b). For the qu...

Thanks for the detailed response!  I ended up doing a numerical answer, asked for m then n in two different questions, and provided bounds on m and n so that each answer is unique. Reading your answer...

In a quiz about gcd, I'd like the students to come up with the factors in Bezout's identity. Namely, for a and b in N, there exist n and m in Z such that an + bm = gcd(a,b). For the qu...