n次乘、开方去9余数验算法

求相同因数乘积的运算叫做乘方;求一个数方根的运算叫做开方。乘方与开方运算可用珠算,亦可用笔算,但运算过程比较烦琐,稍不当心就容易出错,因此答数需要检查,而检查的方式往往复算,甚至多次复算,这是非常乏味的。现介绍一种简捷的"去9余数验算法",不论是多少次乘、开方运算,只要按此法验算,     

ON THE GENERALIZATIONS OF KALANDIA＇S LEMMA

Based on Bernstein＇s Theorem, Kalandia＇s Lemma describes the error estimate and the smoothness of the remainder under the second part of Hoelder norm when a HSlder function is approximated by its best polynomial approximation. In this paper, Kalandia＇s Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Hoeder norm or the weighted HSlder norms.     

珠心算除法练习的数字选择

为了方便快速检验珠心算除法计算结果是否正确,向大家推荐几个组合,利用这些组合进行珠心算除法练习,可以迅速检验计算结果是否正确。一、111÷37的组合(一)任何111的倍数除以37都可以整除,且商都是     

NOTES ON GLAISHER＇S CONGRUENCES

Let p be an odd prime and let n≥1,k≥0 and r be integers,denote by Bk the kth Bernoulli number,It is proved that(i) If r≥1 is odd and suppose 1≥r+4,then ∑j=1^p-1 1/(np+j)^r=-(2n+1)r(r+1)/2(r+2)Bp-r-2p^2(mod p^3).(ii)If r≥2 is even and suppose p≥r+3, then p-1∑j=1 1/(np+j)^r=r/r+1Bv-r-1p(mod P^2).(iii) p-1∑j=1 1/(np+j)p-2=-(2n+1)p(mod P^2).This result generalizes the Glaisher‘s congruence. As a corollary, a generalization of the Wolsten-holme‘s theorem is obtained.     

同余数问题与椭圆曲线

1 同余数是什么。边为整数X，Y，Z的直角三角形，其中(X，Y，Z)称为一组“毕达哥拉斯三元组”．在古希腊就已经由毕达哥拉斯、欧几里得与丢番图等人研究过．我国古代周髀算经之商高定理。     

特殊图形上的顶点坐标

例1(2010年湖北武汉)如图1,所有正方形的中心均在坐标原点,且各边与x轴或y轴平行,从内到外,它们的边长依次为2,4,6,8,…,顶点依次用A1,A2,A3,A4…表示,则顶点A55的坐标为