Putnam's problem

Putnam's problem revolves around understanding whether a G.C.D. (greatest common divisor) function behaves predictably when applied repeatedly to a set of numbers. Specifically, it asks: if you take several numbers, find their G.C.D., then replace each original number with that G.C.D., and repeat this process, does the sequence of G.C.D.s stabilize or follow a pattern? The question explores the long-term behavior of this iterative operation, revealing insights into the structure and relationships among integers within number theory.