abundant number

简明释义

过剩数

英英释义

例句

1.In mathematics, an abundant number is a number for which the sum of its proper divisors is greater than the number itself.

在数学中，丰盈数是指其所有真因子的和大于它本身的数字。

2.Many abundant numbers can be found in the sequence of even integers.

许多丰盈数可以在偶数序列中找到。

3.The concept of abundant numbers is useful in number theory and has applications in cryptography.

丰盈数的概念在数论中很有用，并且在密码学中有应用。

4.In programming, we can write a function to check if a number is abundant number.

在编程中，我们可以编写一个函数来检查一个数字是否为丰盈数。

5.The smallest abundant number is 12, as its divisors (1, 2, 3, 4, 6) add up to 16.

最小的丰盈数是12，因为它的因子（1、2、3、4、6）的和为16。

作文

In the realm of mathematics, particularly in number theory, the concept of an abundant number is quite fascinating and significant. An abundant number is defined as a positive integer that is smaller than the sum of its proper divisors, excluding itself. This means that if you take all the divisors of a number (except the number itself) and add them together, the total will exceed the original number. For example, consider the number 12. Its proper divisors are 1, 2, 3, 4, and 6. When we sum these divisors, we get 1 + 2 + 3 + 4 + 6 = 16, which is greater than 12. Therefore, 12 is classified as an abundant number.The study of abundant numbers dates back to ancient times, with mathematicians like Euclid and later, the great number theorist, Carl Friedrich Gauss, exploring their properties. The interest in abundant numbers is not merely academic; it has implications in various fields, including cryptography, computer science, and even in the understanding of natural phenomena.One of the intriguing aspects of abundant numbers is their relationship with perfect and deficient numbers. A perfect number is one where the sum of its proper divisors equals the number itself, such as 6 (where 1 + 2 + 3 = 6). On the other hand, a deficient number is one where the sum of its proper divisors is less than the number. The classification of numbers into these categories helps mathematicians understand the distribution of integers and their properties better.Moreover, abundant numbers have unique characteristics that make them interesting for exploration. For instance, the smallest abundant number is 12, and as we progress, we find that there are infinitely many abundant numbers. They become increasingly frequent as we move along the number line, which leads to deep mathematical investigations into their density and distribution.In practical applications, the concept of abundant numbers can be seen in various algorithms and computational methods. For example, when designing algorithms for factorization or when analyzing the behavior of certain mathematical functions, understanding the properties of abundant numbers can provide insights that enhance efficiency and performance.Furthermore, the existence of abundant numbers also raises questions about their role in number theory and the broader implications for mathematics as a whole. For instance, the study of these numbers has led to numerous conjectures and theorems that seek to explain their properties and relationships with other classes of numbers.In conclusion, the notion of an abundant number is a rich and complex topic within mathematics. It not only provides a window into the nature of integers but also connects to various branches of mathematical research and application. Understanding abundant numbers allows us to appreciate the beauty and intricacies of mathematics, inspiring further exploration and discovery in this timeless field.

在数学的领域，特别是在数论中，‘丰数’这个概念是相当迷人且重要的。‘丰数’被定义为一个正整数，它小于其所有真因子（不包括自身）的和。这意味着，如果你取一个数的所有因子（除了这个数本身），并将它们加在一起，结果将超过原始数字。例如，考虑数字12。它的真因子是1、2、3、4和6。当我们将这些因子相加时，得到1 + 2 + 3 + 4 + 6 = 16，这大于12。因此，12被归类为‘丰数’。对‘丰数’的研究可以追溯到古代，数学家如欧几里得以及后来的伟大数论学家卡尔·弗里德里希·高斯探索了它们的性质。对‘丰数’的兴趣不仅仅是学术性的；它在多个领域都有影响，包括密码学、计算机科学，甚至在自然现象的理解中。‘丰数’的一个引人入胜的方面是它与完美数和不足数之间的关系。完美数是指其真因子的和等于该数本身的数字，例如6（1 + 2 + 3 = 6）。另一方面，不足数是指其真因子的和小于该数字的数。将数字分类为这些类别有助于数学家更好地理解整数及其属性的分布。此外，‘丰数’具有独特的特征，使其成为探索的有趣对象。例如，最小的‘丰数’是12，随着我们向前推进，我们发现有无限多个‘丰数’。它们在数轴上变得越来越频繁，这导致了对它们的密度和分布的深入数学研究。在实际应用中，‘丰数’的概念可以在各种算法和计算方法中看到。例如，在设计因式分解算法或分析某些数学函数的行为时，理解‘丰数’的属性可以提供增强效率和性能的见解。此外，‘丰数’的存在还引发了关于它们在数论中的角色以及对整个数学的更广泛影响的问题。例如，对这些数字的研究导致了众多猜想和定理，试图解释它们的性质以及与其他数字类别的关系。总之，‘丰数’的概念是数学中一个丰富而复杂的话题。它不仅为我们提供了一个窗口，了解整数的本质，还与数学研究和应用的各个分支相连接。理解‘丰数’使我们能够欣赏数学的美丽和复杂性，激励进一步的探索和发现这一永恒领域。