正整数

Hua Luo—geng [1] has proved the generalized Opial ineguality: where y is an absolutely continuous function on,y=o and l is a positive integer.

华罗庚先生[1]证明了当y是上绝对连续函数，y=O时，推广的opial不等式对正整数ι都成立。

In additive prime number theory,a classical result of Hua states that,every suffi-ciently large odd number N can be represented as 〓,where 〓 is aninteger and 〓 are primes,which can be regarded as an extension of Goldbach-Vinogradov Theorem.

堆垒素数论中一个经典的结果是华罗庚教授证明的：任一个充分大的奇数N都可以表为N=〓+〓+〓，其中λ是一正整数，p1，p2，p3是素数，这一结果可以看作著名的Goldbach-Vinogradov定理的推广。

In the litereture [2], Zhang Zhongfu introduced the conception of adjacent vertex distinguishing total coloring.

在文献[2]中张忠辅等提出了图的邻点可区别全染色的概念，即：设G是阶至少为2的连通简单图，k是正整数，f是V∪E到{1，2，…，k}的映射。

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

The second routine that we will examine is strcmp, which compares the character strings s and t, and returns negative, zero or positive if s is lexicographically less than, equal to, or greater than t.

我们研究的第二个函数是字符串比较函数strcmp。该函数比较字符串s和t，并且根据s按照字典顺序小于、等于或大于t的结果分别返回负整数、0或正整数。

In arithmetic the positive integer and the positive fraction were sufficient for all requirements.

在算数中，曾经正整数和正分数能够满足所有的需求。

Enter a positive integer, the output from one to the integer array of the whole.

详细说明：输入一个正整数，输出从一到这个整数的全排列。

Positive integer and negative integer-one correspondence between:+1 and -1,+2 and -2,+3 and -3,.....

正整数与负整数之间一一对应：＋1与－1，＋2与－2，＋3与－3，…。。。

The digital root of a positive integer is found by summing the digits of the integer .

正整数的数根可以用此整数各位数数字的和来求。

In C under the TSA Sanchez Theorem : A sum of the cube can be written a bunch of odd that the sum...

在C下实现的尼科梅切斯定理：任何一个整数的立方都可以写成一串奇数之和即任意一个正整数n的立方分解成个连续的n个奇数之和。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。