Geodesic
Ternary quadratic forms $ax^2+by^2+cz^2$ representing all positive integers $8k+4$
Kenneth S. Williams 1
1 School of Mathematics and Statistics Carleton University Ottawa, Ontario, Canada K1S 5B6
Acta Arithmetica, Tome 166 (2014) no. 4, pp. 391-396 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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     title = {Ternary quadratic forms $ax^2+by^2+cz^2$
 representing all positive integers $8k+4$},
     journal = {Acta Arithmetica},
     pages = {391--396},
     year = {2014},
     volume = {166},
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     doi = {10.4064/aa166-4-4},
     language = {en},
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 representing all positive integers $8k+4$
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 representing all positive integers $8k+4$
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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

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