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

• Autorzy: Kenneth S. Williams
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11E20: General ternary and quaternary quadratic forms; forms of more than two variables
• 11E25: Sums of squares and representations by other particular quadratic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 4
• Strony: 391-396

Daty

wydano

2014

Twórcy

autor

Kenneth S. Williams

• School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

Identyfikatory

DOI

10.4064/aa166-4-4