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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 ).
The three factor-pairs of 18 are (1, 18), (2, 9), and (3, 6). All three factor pairs will produce triples using the above equations. s = 1, t = 18 produces the triple [7, 24, 25] because x = 6 + 1 = 7, y = 6 + 18 = 24, z = 6 + 1 + 18 = 25. s = 2, t = 9 produces the triple [8, 15, 17] because x = 6 + 2 = 8, y = 6 + 9 = 15, z = 6 + 2 + 9 = 17.
More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...
Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...
Two numbers with the same "abundancy" form a friendly pair; ... 45: 78: 26/15 46: 72: 36/23 47: ... at least one of the prime factors must be congruent to 1 modulo 3 ...
2.45 Primes of the form n 4 + 1. ... 15 p − 1 ≡ 1 (mod p 2): ... Table of prime factors; Wieferich pair; References External links. All ...
Cynthia Erivo says she co-wrote a song for “Wicked” sequel: 'I don't know if you're ready for it'
For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4) .