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Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...
The digit sum of the binary representation of a number is known as its Hamming weight or population count; algorithms for performing this operation have been studied, and it has been included as a built-in operation in some computer architectures and some programming languages. These operations are used in computing applications including ...
Arithmetic progression. An arithmetic progression or arithmetic sequence ( AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13 ...
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. [2] The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows two columns of three apples and two apples ...
An integer is the number zero (), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
Therefore, the theorem states that it is expressible as the sum of two squares. Indeed, 2450 = 72 + 492 . The prime decomposition of the number 3430 is 2 · 5 · 7 3. This time, the exponent of 7 in the decomposition is 3, an odd number. So 3430 cannot be written as the sum of two squares.
Digital root. The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
The Goldbach conjecture for practical numbers, a prime-like sequence of integers, was stated by Margenstern in 1984, and proved by Melfi in 1996: every even number is a sum of two practical numbers. Harvey Dubner proposed a strengthening of the Goldbach conjecture that states that every even integer greater than 4208 is the sum of two twin ...
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