Definition
Let X be a non-negative integer. X is a Kaprekar number for base b if there exist non-negative integers n, A, and positive number B satisfying:
- X² = Abn + B, where 0 < B < bn
- X = A + B
Note that X is also a Kaprekar number for base bn, for this specific choice of n. More narrowly, we can define the set K(N) for a given integer N as the set of integers X for which
- X² = AN + B, where 0 < B < N
- X = A + B
Each Kaprekar number X for base b is then counted in one of the sets K(b), K(b²), K(b³),….
Read more about this topic: Kaprekar Number
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)