Jangwon Ju

most citedThe pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

1 citations · 1 across the 2 of their papers we have counts for

collaborators

5 papers

math.NT2020★ 1 cited

The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

Jangwon Ju, Daejun Kim

In this article, we study the representability of integers as sums of pentagonal numbers, where a pentagonal number is an integer of the form $P_{5} (x) = \frac{3 x ^{2} - x}{2}$ for some non…

math.NT2020

Prime-universal diagonal quadratic forms

Jangwon Ju, Daejun Kim, Kyoungmin Kim +2

A (positive definite and integral) quadratic form is said to be $prime-universal$ if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-uni…

math.NT2020

Ternary quadratic forms representing same integers

Jangwon Ju

In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isom…

math.NT2018

Universal mixed sums of generalized $4$ - and $8$ -gonal numbers

Jangwon Ju, Byeong-Kweon Oh

An integer of the form $P_{m} (x) = \frac{( m - 2 ) x ^{2} - ( m - 4 ) x}{2}$ for an integer $x$ , is called a generalized $m$ -gonal number. For positive integers $α_{1}, \dots, α_{u}$ and $β_{1}, \dots, β_{v}$ ,…

math.NT2018

Universal sums of generalized pentagonal numbers

Jangwon Ju

For an integer $x$ , an integer of the form $P_{5} (x) = \frac{3 x ^{2} - x}{2}$ is called a generalized pentagonal number. For positive integers $α_{1}, \dots, α_{k}$ , a sum $Φ_{α_1,\dots,α_k}(x_1,x_…

The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

Prime-universal diagonal quadratic forms

Ternary quadratic forms representing same integers

Universal mixed sums of generalized 4- and 8-gonal numbers

Universal sums of generalized pentagonal numbers

Universal mixed sums of generalized $4$ - and $8$ -gonal numbers