Displaying similar documents to “A generalization of the question of Sierpiński on geometric progressions.”

A note on two linear forms

Nikolay Moshchevitin (2014)

Acta Arithmetica

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We prove a result on approximations to a real number θ by algebraic numbers of degree ≤ 2 in the case when we have certain information about the uniform Diophantine exponent ω̂ for the linear form x₀ + θx₁ + θ²x₂.

Parametric Solutions of the Diophantine Equation A² + nB⁴ = C³

Susil Kumar Jena (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.