In number theory, Znam's problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znam's problem is named after the Slovak mathematician Stefan Znam, who suggested it in 1972, although other mathematicians had considered similar problems around the same time. One closely related problem drops the assumption of properness of the divisor, and will be called the improper Znam problem hereafter.One solution to the improper Znam problem is easily provided for any k: the first k terms of Sylvester's sequence have the required property. Sun (1983) showed that there is at least one solution to the (proper) Znam problem for each k ? 5. Sun's solution is based on a recurrence similar to that for Sylvester's sequence, but with a different set of initial values.

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