Displaying similar documents to “The Diophantine equation x y + y z + x z = n and indecomposable binary quadratic forms.”

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

Kenneth S. Williams (2014)

Acta Arithmetica

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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.