Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4

Kenneth S. Williams. "Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4." Acta Arithmetica 166.4 (2014): 391-396. <http://eudml.org/doc/278890>.

@article{KennethS2014,
abstract = {Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.},
author = {Kenneth S. Williams},
journal = {Acta Arithmetica},
keywords = {ternary quadratic form; representation of integers},
language = {eng},
number = {4},
pages = {391-396},
title = {Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4},
url = {http://eudml.org/doc/278890},
volume = {166},
year = {2014},
}

TY - JOUR
AU - Kenneth S. Williams
TI - Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4
JO - Acta Arithmetica
PY - 2014
VL - 166
IS - 4
SP - 391
EP - 396
AB - Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.
LA - eng
KW - ternary quadratic form; representation of integers
UR - http://eudml.org/doc/278890
ER -