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[2] [3] J.Ward [4] proved that any positive integer other than 10 with abundancy index 9/5 must be a square with at least six distinct prime factors, the smallest being 5. Further, at least one of the prime factors must be congruent to 1 modulo 3 and appear with an exponent congruent to 2 modulo 6 in the prime power factorization of n ...
The difference of two squares is used to find the linear factors of the sum of two squares, using complex number coefficients. For example, the complex roots of z 2 + 4 {\displaystyle z^{2}+4} can be found using difference of two squares:
The elements 2 and 1 + √ −3 are two maximal common divisors (that is, any common divisor which is a multiple of 2 is associated to 2, the same holds for 1 + √ −3, but they are not associated, so there is no greatest common divisor of a and b.
99 is: a composite number; a square-prime, of the form (p 2, q). It is the 11th composite number of this form and the third of the form (3 2, q). It has an aliquot sum of 57, within an aliquot sequence of two composite numbers (99,57,23,1,0), to the Prime in the 23-aliquot tree. a Kaprekar number [1] a lucky number; a palindromic number in base ten
Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
Image source: The Motley Fool. Yum China (NYSE: YUMC) Q4 2024 Earnings Call Feb 06, 2025, 7:00 a.m. ET. Contents: Prepared Remarks. Questions and Answers. Call ...
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).
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