Let A and B be sets. Assume ZF without assuming choice. Then, for all non negative integers n, I believe (correct me if I'm wrong) that, if n x A is equipotent to n x B, then A is equipotent to B. There's a famous Conway/Doyle paper which proves this for n = 2 and n = 3. However, it doesn't seem rigorous or clear and I have trouble understanding it.
Does anyone know a more axiomatic treatment? (I don't have access to a university, and I'm not in the market for maths purchases, so only free references would be helpful.)