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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-4,
author = {Kenneth S. Williams},
title = {Ternary quadratic forms ax$^2$ + by$^2$ + cz$^2$ representing all positive integers 8k + 4},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {391-396},
zbl = {1327.11023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-4}
}
Kenneth S. Williams. Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4. Acta Arithmetica, Tome 166 (2014) pp. 391-396. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa166-4-4/