Erdős Problem #981
The statement as posed is true, and a proof exists.
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Property of a natural \(N\) to satisfy \(\sum_{n\leq N} \left(\frac{n}{p}\right)<\epsilon N\), where \(\left(\frac{n}{p}\right)\) is the Jacobi symbol. The theorem statement mentions Legendre symbol, however in formalization we use Jacobi symbol to avoid problem with passing the fact that \(p\) is prime. For prime \(p\) `jacobiSym n p = legendreSym p n`.
The smallest integer \(m\) such that \(\sum_{n\leq N} \left(\frac{n}{p}\right)<\epsilon N\) for all \(N\geq m\).
The smallest integer \(m\) such that \(\sum_{n\leq m} \left(\frac{n}{p}\right)<\epsilon m\)
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