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1956 AMC 12 Question 36

AMC12 · 1956 AMC 12

Question 36

If the sum $1+2+3+\cdots+K$ is a perfect square $N^2$ and if $N$ is less than $100,$ then the possible values for $K$ are:
  1. only $1$
  2. $1$ and $8$
  3. only $8$
  4. $8$ and $49$
  5. $1,$ $8,$ and $49$