Daejun Kim

We say a positive integer n satisfies the Lehmer property if <TEX>${\phi}(n)$</TEX> divides n - 1, where <TEX>${\phi}(n)$</TEX> is the Euler's totient function. Clearly, every prime satisfies the Lehmer property. No composite integer satisfying the Lehmer property is known. In this article, we show that every composite integer of the form <TEX>$D_{p,n}=np^n+1$</TEX>, for a prime p and a positive integer n, or of the form <TEX>${\alpha}2^{\beta}+1$</TEX> for <TEX>${\alpha}{\leq}{\beta}$</TEX> doe

Abstract In December 2007, the 17,500-metric ton, Arthit PP deck was installed over the substructure in a single piece by a using J. Ray McDermott's (J. Ray) transportation and installation barge Intermac-650 (I-650), specially designed for float-over installation. The Arthit Field is located in the Gulf of Thailand in 80 meters of water. A number of technical challenges were overcome to accomplish the successful and safe float-over. A single-piece deck installation using the float-over techniqu

Abstract Lifting problem for universal quadratic forms asks for totally real number fields that admit a positive definite quadratic form with coefficients in that is universal over the ring of integers of . In this paper, we show is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.

We consider weighted sums of generalized polygonal numbers with coefficients $1$ or $2$. We show that for any $m\ge 10$, a weighted sum of generalized $m$-gonal numbers represents every non-negative integer if it represents $1$, $m-4$, and $m-2$. Furtherm

Abstract A (positive definite and integral) quadratic form is said to be prime-universal if it represents all primes. Recently, Doyle and Williams [‘Prime-universal quadratic forms $ax^2+by^2+cz^2$ and $ax^2+by^2+cz^2+dw^2$ ’, Bull. Aust. Math. Soc. 101 (2020), 1–12] classified all prime-universal diagonal ternary quadratic forms and all prime-universal diagonal quaternary quadratic forms under two conjectures. We classify all prime-universal diagonal quadratic forms regardless of rank, and prov

Finding all integers which can be written as a sum of three nonzero squares of integers has been studied by a number of authors. This question is solved under the assumption of the Generalized Riemann Hypothesis (GRH), but still remains unsolved unconditionally. In this paper, we show that out of all integers that are sums of three squares, all but finitely many can be written as [Formula: see text] for some integers [Formula: see text]. Furthermore, we explicitly describe this finite set under

Abstract In this paper, we consider the solvability over non-negative integers of certain Diophantine equations coming from representations of integers as sums of pentagonal numbers (counting the number of dots in a regular pentagon). We study a general method to obtain generalized versions of Cauchy’s lemma. Using this, we show the “pentagonal theorem of 63”, which states that a sum of pentagonal numbers represents every non-negative integer if and only if it represents the integers <m:math xml

Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\mathbb{Q}(ζ_7+ζ_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.

Objectives : The present study has been undertaken to investigate the effects of Carthami Semen and Jogyeongjongok-Tang on pregnant rats. Method : In this experiment, the pregnant rats were administered by water extracts of Carthami Semen and Jogyeongjongok-Tang. The levels of weights, ALT, AST, ALP, BUN, creatinine, progesterone, Na and K in serum and reproductive indices of the rats were measured after treatment. Results : The levels of body weight gains were not significantly changed in compa