## Integer sequences having prescribed quadratic character

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- by D. H. Lehmer, Emma Lehmer and Daniel Shanks PDF
- Math. Comp.
**24**(1970), 433-451 Request permission

## Abstract:

For the odd primes ${p_1} = 3,$, ${p_2} = 5, \cdots ,$ we determine integer sequences ${N_p}$ such that the Legendre symbol $({N \left / {\vphantom {N {{p_i}}}} \right . {{p_i}}}) = \pm 1$ for all ${p_i} \leqq p$ for a prescribed array of signs $\pm 1$; (i.e., for a prescribed quadratic character). We examine six quadratic characters having special interest and applications. We present tables of these ${N_p}$ and examine some applications, particularly to questions concerning extreme values for the smallest primitive root (of a prime $N$), the class number of the quadratic field $R(\surd - N)$, the real Dirichlet $L$ functions, and quadratic character sums.## References

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## Additional Information

- © Copyright 1970 American Mathematical Society
- Journal: Math. Comp.
**24**(1970), 433-451 - MSC: Primary 10.03
- DOI: https://doi.org/10.1090/S0025-5718-1970-0271006-X
- MathSciNet review: 0271006