• 대한수학회보
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• 제52권3호
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• pp.699-705
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• 2015

Two well known facts from elementary number theory are proven by using Bergman spaces.

• 대한수학회논문집
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• 제19권2호
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• pp.205-210
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• 2004

According to Diriclet's Theorem, there are infinitely many primes of the form An+ 1 for any fixed positive integer A. For this, there already exists a classical simple proof using cyclotomic polynomials. In this paper, we develop another elementary proof of this statement.

• 대한수학회논문집
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• 제20권3호
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• pp.467-485
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• 2005

Let p and q be odd primes with p=2q+1. We study the number of solutions of congruence equations $ax^i\;+\;by^j\;{\equiv}\;c$ (mod p) and a$ax^i\;+\;by^j\;+\;dz^t\;{\equiv}\;c(modp)$

• 대한수학회지
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• 제57권5호
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• pp.1061-1078
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• 2020

We prove some results about the finiteness of co-associated primes of generalized local homology modules inspired by a conjecture of Grothendieck and a question of Huneke. We also show some equivalent properties of minimax local homology modules. By duality, we get some properties of Herzog's generalized local cohomology modules.

• 호남수학학술지
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• 제30권1호
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• pp.101-113
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• 2008

Let M be an arbitrary module over a commutative Noetherian ring R and let ${\triangle}$ be a multiplicatively closed set of non-zero ideals of R. In this paper, we will introduce the dual notion of ${\triangle}$-closure and ${\triangle}$-dependence of an ideal with respect to M and obtain some related results.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• 대한수학회보
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• 제55권5호
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• pp.1371-1387
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• 2018

The classification of the self-dual codes over Galois rings GR(p, 2) and $GR(p^2,2)$ of length 4 is completed for all primes p up to equivalence in terms of automorphism group. We obtain all inequivalent classes and the number of each classes of self-dual codes for all primes.

• 충청수학회지
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• 제27권3호
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• pp.427-431
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• 2014

In this paper, we show that groups of order $2^npq$, where p, q are primes of the from $p=2^n-1$, $q=2^{n-1}+p$ with $n{\geq}3$, are not simple and groups of order $2^npq^t$ for $t{\geq}2$, where p, q are odd primes of the form $p=2^m-1$, $q=2^n-1$ with m < n, are not simple.

• 대한수학회보
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• 제60권3호
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• pp.775-783
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• 2023

Van Hamme's (G.2) supercongruence modulo p⁴ for primes p ≡ 3 (mod 4) and p > 3 was first established by Swisher. A q-analogue of this supercognruence was implicitly given by the first author and Schlosser. In this paper, we present a new q-analogue of Van Hamme's (G.2) supercongruence for p ≡ 3 (mod 4).

• 대한수학회논문집
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• 제38권3호
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• pp.715-723
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• 2023

In this paper, we construct explicitly an infinite family of primes P with h^±_P ≡ 0 (mod q^{deg P}), where h^±_P are the plus and minus parts of the divisor class number of the P-th cyclotomic function field over 𝔽_q(T). By using this result and Dirichlet's theorem, we give a condition of A, M ∈ 𝔽_q[T] such that there are infinitely many primes P satisfying with h^±_P ≡ 0 (mod p^e) and P ≡ A (mod M).