• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.149-157
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• 1997

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1427-1437
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• 2023

It is known that the automorphism group of a K3 surface with Picard number two is either an infinite cyclic group or an infinite dihedral group when it is infinite. In this paper, we study the generators of such automorphism groups. We use the eigenvector corresponding to the spectral radius of an automorphism of infinite order to determine the generators.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.327-334
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• 2021

In this paper, we find all the prime numbers p that satisfy the following statement. If a positive integer k is a divisor of p - 1, then there is a sequence consisting of all k-th power residues modulo p, satisfying the recurrence equation of the Fibonacci sequence modulo p.

• Journal for History of Mathematics
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• v.16 no.1
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• pp.17-24
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• 2003

The Pythagorean equation $x^2{＋}y^2{=}z^2$ and Pythagorean triple had appeared in the Babylonian clay tablet made between 1900 and 1600 B. C. Another quadratic equation called Pell equation was implicit in an Archimedes' letter to Eratosthenes, so called ‘cattle problem’. Though elliptic equation were contained in Diophantos’ Arithmetica, a substantial progress for the solution of cubic equations was made by Bachet only in 1621 when he found infinitely many rational solutions of the equation $y^2{=}x^3{-}2$. The equation $y^2{=}x^3{+}c$ is the simplest of all elliptic equations, even of all Diophantine equations degree greater than 2. It is due to Bachet, Dirichlet, Lebesque and Mordell that the equation in better understood.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.209-219
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• 2021

A set {a₁, a₂, ⋯ , a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. Let F_n be the nth Fibonacci number which is defined by F₀ = 0, F₁ = 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.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.533-538
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• 2022

Cryptography is one of the most essential developing areas, which deals with the secure transfer of messages. In recent days, there are more number of algorithms have been evolved to provide better security. This work is also such an attempt. In this paper, an algorithm is presented for encryption and decryption which employs the matrix Q^p* and the well- known equation x² - py² = 1 where p is a prime.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.425-445
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• 2018

A set {$a_1,\;a_2,{\ldots},\;a_m$} of positive integers is called a Diophantine m-tuple if $a_ia_j+1$ is a perfect square for all $1{\leq}i$ < $j{\leq}m$. In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs {$F_{k-2}F_{k+1},\;F_{k-1}F_{k+2}$} and {$F_{k-2}F_{k-1},\;F_{k+1}F_{k+2}$}, where $F_n$ is the n-th Fibonacci number.