For how many positive integers $p$ does there exist a triangle with sides of length $3p-1,$ $3p,$ and $p^2 + 1?$
Question:
For how many positive integers $p$ does there exist a triangle with sides of length $3p-1,$ $3p,$ and $p^2 + 1?$
Answer:
Let's think step by step.

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For how many positive integers $p$ does there exist a triangle with sides of length $3p-1,$ $3p,$ and $p^2 + 1?$
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