杨辉三角的若干性质研究

Some Properties of Yang Hui's Triangle

杨辉三角是二项式系数在三角形中的一种几何排列,通过初等方法及同余运算对杨辉三角中数的奇偶性进行进一步研究,得出杨辉三角中第a行的二项式系数中可被素数p整除的个数,第0行至第a行构成的三角中可被素数p整除的个数,以及每一斜列上的二项式系数中可被素数p整除的个数。

Yang Hui＇s triangle is a kind of geometric arrangement of binomial coefficients in a triangle. Further research on this issue was studied by elementary methods and congruence arithmetic in this paper,and came to the conclusions that the numbers of binomial coefficients of Yang Hui＇s triangle in row a which was divisible by prime number p,the numbers of triangles from line0 to line a which was divisible by prime number p,and the number of binomial coefficients on each seleme which was divisible by prime number p.