Geodesic
Ternary quadratic forms $ax^2+by^2+cz^2$ representing all positive integers $8k+4$
Kenneth S. Williams1
1 School of Mathematics and Statistics Carleton University Ottawa, Ontario, Canada K1S 5B6
Acta Arithmetica, Tome 166 (2014) no. 4, pp. 391-396.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Under the assumption that the ternary form $x^2+2y^2+5z^2+xz$ represents all odd positive integers, we prove that a ternary quadratic form $ax^2+by^2+cz^2$ $(a,b,c \in \mathbb {N})$ represents all positive integers $n\equiv 4\ ({\rm mod}\ 8)$ if and only if it represents the eight integers $4,12,20,28,52,$ $60,140$ and $308$.
DOI : 10.4064/aa166-4-4
Keywords: under assumption ternary form represents odd positive integers prove ternary quadratic form mathbb represents positive integers equiv mod only represents eight integers

Kenneth S. Williams 1

1 School of Mathematics and Statistics Carleton University Ottawa, Ontario, Canada K1S 5B6 
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Kenneth S. Williams. Ternary quadratic forms $ax^2+by^2+cz^2$
 representing all positive integers $8k+4$. Acta Arithmetica, Tome 166 (2014) no. 4, pp. 391-396. doi : 10.4064/aa166-4-4. http://geodesic.mathdoc.fr/articles/10.4064/aa166-4-4/

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