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1961 AMC 12 Question 4

AMC12 · 1961 AMC 12

Question 4

Let the set consisting of the squares of the positive integers be called $u;$ thus $u$ is the set $1,$ $4,$ $9,$ $\ldots.$ If a certain operation on one or more members of the set always yields a member of the set, we say that the set is closed under that operation. Then $u$ is closed under:
  1. addition
  2. multiplication
  3. division
  4. extraction of a positive integral root
  5. none of these