𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Bounds of quadratic residues in arithmetic progression

✍ Scribed by Sahib Singh


Publisher
Elsevier Science
Year
1970
Tongue
English
Weight
255 KB
Volume
2
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.


πŸ“œ SIMILAR VOLUMES


Abelian groups and quadratic residues in
✍ Emil JeΕ™Γ‘bek πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 282 KB

We investigate the provability of some properties of abelian groups and quadratic residues in variants of bounded arithmetic. Speci cally, we show that the structure theorem for nite abelian groups is provable in ), and use it to derive Fermat's little theorem and Euler's criterion for the Legendre

Arithmetic Progressions in Sequences wit
✍ Tom C Brown; Donovan R Hare πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 528 KB

Let G(k, r) denote the smallest positive integer g such that if 1=a 1 , a 2 , ..., a g is a strictly increasing sequence of integers with bounded gaps a j+1 &a j r, 1 j g&1, then [a 1 , a 2 , ..., a g ] contains a k-term arithmetic progression. It is shown that G(k, 2) > -(k & 1)Γ‚2 ( 43 ) (k&1)Γ‚2 ,

Discrepancy of Arithmetic Progressions i
✍ Benedek ValkΓ³ πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 136 KB

proved that the discrepancy of arithmetic progressions contained in [1, N]={1, 2, ..., N} is at least cN 1/4 , and later it was proved that this result is sharp. We consider the d-dimensional version of this problem. We give a lower estimate for the discrepancy of arithmetic progressions on [1, N] d