The Equivalence of Two Conjectures in the Theory of Numrers

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Authors

  • University of Illinois ,US
  • University of Colorado ,US

DOI:

https://doi.org/10.18311/jims/1953/17031

Abstract

The equivalence of these two conjectures can even be put in the following sharper form : If N is any positive integer, Conjecture I is true for all n ≤ N if and only if Conjecture II is true for all n ≤ N and all real characters x. In one direction this is trivial, since λ(v) = (v|N*)forv= 1,2,..., N, where (x | y) denotes the Legendre- Jacobi symbol and N* denotes the smallest positive integer such that (p | N*) = - 1 for all primes p not exceeding N.

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Published

1953-12-01

How to Cite

Bateman, P. T., & Chowla, S. (1953). The Equivalence of Two Conjectures in the Theory of Numrers. The Journal of the Indian Mathematical Society, 17(4), 177–181. https://doi.org/10.18311/jims/1953/17031