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DIOPHANTINE TRIPLE WITH FIBONACCI NUMBERS AND ELLIPTIC CURVE
Park, Jinseo Korean Mathematical Society 2021 대한수학회논문집 Vol.36 No.3
A Diophantine m-tuple is a set {a<sub>1</sub>, a<sub>2</sub>, …, a<sub>m</sub>} of positive integers such that a<sub>i</sub>a<sub>j</sub>+1 is a perfect square for all 1 ≤ i < j ≤ m. Let E<sub>k</sub> be the elliptic curve induced by Diophantine triple {F<sub>2k</sub>, 5F<sub>2k+2</sub>, 3F<sub>2k</sub> + 7F<sub>2k+2</sub>}. In this paper, we find the structure of a torsion group of E<sub>k</sub>, and find all integer points on E<sub>k</sub> under assumption that rank(E<sub>k</sub>(ℚ)) = 1 and some further conditions.
INTEGER POINTS ON THE ELLIPTIC CURVES INDUCED BY DIOPHANTINE TRIPLES
Park, Jinseo Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
A set {a<sub>1</sub>, a<sub>2</sub>, …, a<sub>m</sub>} of positive integers is called a Diophantine m-tuple if a<sub>i</sub>a<sub>j</sub> + 1 is a perfect square for all 1 ≤ i < j ≤ m. In this paper, we find the structure of a torsion group of elliptic curves E<sub>k</sub> constructed by a Diophantine triple {F<sub>2k</sub>, F<sub>2k+2</sub>, 4F<sub>2k+1</sub>F<sub>2k+2</sub>F<sub>2k+3</sub>}, and find all integer points on the elliptic curve under assumption that rank(E<sub>k</sub>(ℚ)) = 2.
Park, Jinseo,Rhee, Sangkee American Society for Biochemistry and Molecular Bi 2013 The Journal of biological chemistry Vol.288 No.22
<P>Succinic semialdehyde dehydrogenase (SSADH) from cyanobacterium <I>Synechococcus</I> differs from other SSADHs in the γ-aminobutyrate shunt. <I>Synechococcus</I> SSADH (SySSADH) is a TCA cycle enzyme and completes a 2-oxoglutarate dehydrogenase-deficient cyanobacterial TCA cycle through a detour metabolic pathway. SySSADH produces succinate in an NADP<SUP>+</SUP>-dependent manner with a single cysteine acting as the catalytic residue in the catalytic loop. Crystal structures of SySSADH were determined in their apo form, as a binary complex with NADP<SUP>+</SUP> and as a ternary complex with succinic semialdehyde and NADPH, providing details about the catalytic mechanism by revealing a covalent adduct of a cofactor with the catalytic cysteine in the binary complex and a proposed thiohemiacetal intermediate in the ternary complex. Further analyses showed that SySSADH is an oxidation-sensitive enzyme and that the formation of the NADP-cysteine adduct is a kinetically preferred event that protects the catalytic cysteine from H<SUB>2</SUB>O<SUB>2</SUB>-dependent oxidative stress. These structural and functional features of SySSADH provide a molecular basis for cofactor-dependent oxidation protection in 1-Cys SSADH, which is unique relative to other 2-Cys SSADHs employing a redox-dependent formation of a disulfide bridge.</P>
THE EXTENDIBILITY OF DIOPHANTINE PAIRS WITH FIBONACCI NUMBERS AND SOME CONDITIONS
Jinseo Park 충청수학회 2021 충청수학회지 Vol.34 No.3
A set {a_1, a_2, cdots, a_m} of positive integers is called a Diophantine m-tuple if a_ia_j+1 is a perfect square for all 1leq i < j leq m. Let F_n be the nth Fibonacci number which is defined by F_0=0, F_1=1 and F_{n+2}=F_{n+1}+F_n. In this paper, we find the extendibility of Diophantine pairs {F_{2k}, b} with some conditions.