query: Relationship between positive rational numbers and their ``prime factorization vectors"
positive_passages.docid: 152503
positive_passages.text: Rational numbers as vectors in infinite dimensional space with the basis $( \log 2,\log 3, \log 5, \log 7, \dots, \log p, \dots) $
negative_passages.docid: 117132
negative_passages.text: Rationals of the form $\frac{p}{q}$ where $p,q$ are primes in $[a,b]$
negative_passages.docid: 71572
negative_passages.text: factor-square property (FSP) of polynomials
negative_passages.docid: 105623
negative_passages.text: Prime factorization knowing n and Euler's function
negative_passages.docid: 82075
negative_passages.text: Understanding the trial division primality test
negative_passages.docid: 54128
negative_passages.text: Is it feasible to build an index of prime factors?
negative_passages.docid: 152297
negative_passages.text: Understanding quotients of $\mathbb{Q}[x]$
negative_passages.docid: 95692
negative_passages.text: Factoring polynomials of the form $1+x+\cdots +x^{p-1}$ in finite field
negative_passages.docid: 152506
negative_passages.text: The greatest common divisor is the smallest positive linear combination
negative_passages.docid: 144738
negative_passages.text: Prime factorizations of consecutive numbers, can they both contains powers of greater than or equal to $1000$?
negative_passages.docid: 14827
negative_passages.text: RSA: Fast factorization of N if d and e are known
negative_passages.docid: 155559
negative_passages.text: Quickest way to determine a polynomial with positive integer coefficients
negative_passages.docid: 103165
negative_passages.text: the number of the positive integer numbers $k$ that makes for the two quadratic equations $ \pm x^2 \pm px \pm k$ rational roots.
negative_passages.docid: 158729
negative_passages.text: Are the polynomial remainder and factor theorems equivalent?
negative_passages.docid: 4435
negative_passages.text: What does $\!\bmod(n,x^r-1)$ mean? [in AKS primality test]
negative_passages.docid: 44573
negative_passages.text: Can $\pi$ be rational in some base radix
negative_passages.docid: 78343
negative_passages.text: $4x^2+1$ factors only into $4y+1$ primes