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词汇 Relatively prime
分类 英语词汇 英语翻译词典
释义

Relatively prime

中文百科

互质 Coprime integers

(重定向自Relatively prime)

互质(英文:coprime,符号:⊥,又称互素、relatively prime、mutually prime、co-prime)。在数论中,如果两个或两个以上的整数的最大公因数是 1,则称它们为互质。依此定义:

  • 如果数域是正整数 \mathbb{N^+},那么 1 与所有正整数互质。
  • 如果数域是整数 \mathbb{Z},那么 1-1 与所有整数互质,而且它们是唯一与 0 互质的整数。

两个整数 ab 互质,记为 ab

英语百科

Coprime integers 互质

(重定向自Relatively prime)
Figure 1. The numbers 4 and 9 are coprime. Therefore, the diagonal of a 4 x 9 lattice does not intersect any other lattice points
The order of generation of coprime pairs by this algorithm. First node (2,1) is marked red, its three children are shown in orange, third generation is yellow, and so on in the rainbow order.

In number theory, two integers a and b are said to be relatively prime, mutually prime, or coprime (also spelled co-prime) if the only positive integer that divides both of them is 1. That is, the only common positive factor of the two numbers is 1. This is equivalent to their greatest common divisor being 1. The numerator and denominator of a reduced fraction are coprime. In addition to \***(a, b) = 1\; and (a, b) = 1,\; the notation a\perp b is sometimes used to indicate that a and b are relatively prime.

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