scholarly journals Quadratic Residues and Non-Residues in Arithmetic Progression

2016 ◽  
pp. 227-271
Author(s):  
Steve Wright
Keyword(s):  
Arithmetic Progression ◽  
Quadratic Residues

scholarly journals Five squares in arithmetic progression over quadratic fields

2013 ◽  
Vol 29 (4) ◽  
pp. 1211-1238 ◽  
Author(s):  
Enrique González-Jiménez ◽  
Xavier Xarles
Keyword(s):  
Arithmetic Progression ◽  
Quadratic Fields

scholarly journals SUMS OF PRODUCTS OF CONGRUENCE CLASSES AND OF ARITHMETIC PROGRESSIONS

2009 ◽  
Vol 05 (04) ◽  
pp. 625-634
Author(s):  
SERGEI V. KONYAGIN ◽  
MELVYN B. NATHANSON
Keyword(s):  
Arithmetic Progression ◽  
Congruence Class ◽  
Arithmetic Progressions ◽  
Sum Of Products ◽  
Sums Of Products ◽  
Positive Integers ◽  
Congruence Classes

Consider the congruence class Rm(a) = {a + im : i ∈ Z} and the infinite arithmetic progression Pm(a) = {a + im : i ∈ N0}. For positive integers a,b,c,d,m the sum of products set Rm(a)Rm(b) + Rm(c)Rm(d) consists of all integers of the form (a+im) · (b+jm)+(c+km)(d+ℓm) for some i,j,k,ℓ ∈ Z. It is proved that if gcd (a,b,c,d,m) = 1, then Rm(a)Rm(b) + Rm(c)Rm(d) is equal to the congruence class Rm(ab+cd), and that the sum of products set Pm(a)Pm(b)+Pm(c)Pm eventually coincides with the infinite arithmetic progression Pm(ab+cd).

Heronian Triangles with Sides in Arithmetic Progression: An Inradius Perspective

2012 ◽  
Vol 85 (4) ◽  
pp. 290-294 ◽  
Author(s):  
Herb Bailey ◽  
William Gosnell
Keyword(s):  
Arithmetic Progression

Partitions into kth powers of terms in an arithmetic progression

2018 ◽  
Vol 290 (3-4) ◽  
pp. 1277-1307 ◽  
Author(s):  
Bruce C. Berndt ◽  
Amita Malik ◽  
Alexandru Zaharescu
Keyword(s):  
Arithmetic Progression

scholarly journals Rational tetrahedra with edges in arithmetic progression

2005 ◽  
Vol 111 (1) ◽  
pp. 57-80 ◽  
Author(s):  
C. Chisholm ◽  
J.A. MacDougall
Keyword(s):  
Arithmetic Progression
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