On the Diophantine equation \(y^2=4q^n+4q+1\)

DOI10.1016/0022-314X(86)90092-2zbMath0586.10011MaRDI QIDQ1071797

John Wolfskill, Nicholas Tzanakis

Publication date: 1986

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

higher degree Diophantine equationhypergeometric method[n,k codes over GF(q)]Calderbank's equation

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Higher degree equations; Fermat's equation (11D41)

Related Items (8)

The diophantine equation \(x^ 2=4q^{a/2}+4q+1\), with an application to coding theory ⋮ On the generalized Ramanujan-Nagell equation \(x^2+D=p^z\) ⋮ Starting with gaps between k-free numbers ⋮ On the 430-cap of \(\mathrm{PG}(6,4)\) having two intersection sizes with respect to hyperplanes ⋮ On the diophantine equation \(x^ 2+D=4p^ n\) ⋮ On \(px^{2}+q^{2n}=y^{p}\) and related Diophantine equations ⋮ Intriguing sets in partial quadrangles ⋮ On a conjecture of Ma

Cites Work

• On the Diophantine equation \(y^2-D=2^k\)
• Two-weight ternary codes and the equation \(y^2=4 \times 3^\alpha+13\)
• On Uniformly Packed [n , n -k , 4 Codes over GF(q ) and a Class of Caps in PG(k -1, q )]
• The Integer Points on Three Related Elliptic Curves
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• On the generalized Ramanujan-Nagell equation I
• On the generalized Ramanujan-Nagell equation, II
• On two theorems of Gelfond and some of their applications

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