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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 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 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…