Integral Isosceles Triangle-Parallelogram and Heron triangle-Rhombus Pairs with a Common Area and Common Perimeter [0.03%]
具有相同面积和周长的等腰三角形-平行四边形和海伦三角形-菱形配对
Pradeep Das,Abhishek Juyal,Dustin Moody
Pradeep Das
In this paper we show that there are infinitely many pairs of integer isosceles triangles and integer parallelograms with a common (integral) area and common perimeter. We also show that there are infinitely many Heron triangles and integer...
Integral-valued polynomials over sets of algebraic integers of bounded degree [0.03%]
有界次数代数整数集上的取整系数多项式
Giulio Peruginelli
Giulio Peruginelli
Let K be a number field of degree n with ring of integers [Formula: see text]. By means of a criterion of Gilmer for polynomially dense subsets of the ring of integers of a number field, we show that, if [Formula: see text] maps every eleme...
Sylow p-groups of polynomial permutations on the integers mod [Formula: see text] [0.03%]
模[power]整数上多项式置换的Sylow p群
Sophie Frisch,Daniel Krenn
Sophie Frisch
We enumerate and describe the Sylow p-groups of the groups of polynomial permutations of the integers mod [Formula: see text] for [Formula: see text] and of the pro-finite group which is the projective limit of these groups. ...
Silviu Radu,James A Sellers
Silviu Radu
In 2007, Andrews and Paule introduced the family of functions [Formula: see text] which enumerate the number of broken k-diamond partitions for a fixed positive integer k. Since then, numerous mathematicians have considered partitions congr...