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Before going any further, we need to review some basic notation that will be used in what follows. We usually employ Latin letters to denote unspecified integers. We denote by \(a&gt;b\) Greater than ( \(a\ge b\) Greater than or equal to) that a is greater than b (a is greater than or equal to b). Also, \(a&lt;b_ Less="" than="" _="" _a_le="" b_="" or="" equal="" to_="" means="" that="" a="" is="" less="" b="" _a="" to="" b_.="" As="" examples_="" we="" note="" _5=""&gt;4\) , \(5\ge 4\) , \(4&lt;5\) , \(4\le 5\) . Notice that if \(a\le b\) and \(a\ge b\) , then \(a=b\) ; also, if \(a\ge b\) , then \(-a\le -b\) . We use |x|Absolute value function (the absolute value of x) to denote x when \(x\ge 0\) or \(-x\) when \(x&lt;0\) . Thus, \(|x|\ge 0\) . For example, \(|-5/4|=5/4\) , \(|3/2|=3/2\) .</b_>

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Division, Factors, Primes, Congruences, GCD, etc.

  • 章节

  • 发表日期：

    2025年

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  • Eric L. F. Roettger,
  • Hugh C. Williams

摘要

Before going any further, we need to review some basic notation that will be used in what follows. We usually employ Latin letters to denote unspecified integers. We denote by \(a>b\) Greater than ( \(a\ge b\) Greater than or equal to) that a is greater than b (a is greater than or equal to b). Also, \(a<b_ Less="" than="" _="" _a_le="" b_="" or="" equal="" to_="" means="" that="" a="" is="" less="" b="" _a="" to="" b_.="" As="" examples_="" we="" note="" _5="">4\) , \(5\ge 4\) , \(4<5\) , \(4\le 5\) . Notice that if \(a\le b\) and \(a\ge b\) , then \(a=b\) ; also, if \(a\ge b\) , then \(-a\le -b\) . We use |x|Absolute value function (the absolute value of x) to denote x when \(x\ge 0\) or \(-x\) when \(x<0\) . Thus, \(|x|\ge 0\) . For example, \(|-5/4|=5/4\) , \(|3/2|=3/2\) .