2016年6月24日 · $\begingroup$ "a divides b" means a and b are integers and there is an integer n, such that n x a = b; or ...

Note that the vertical bar character used there is normatively identified as U+2223 DIVIDES (∣), note the common U+007C VERTICAL LINE (|) that we enter directly on a keyboard. It is of course possible to express the same thing using a congruence notation, but only for integers (not e.g. for polynomials). $\endgroup$ –

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Since if n divides both a and b, then it is divisible by something other than itself and 1? Also, did I read that right "n divides ab, implies n divides a or n divides b if and only if n is a prime"? $\endgroup$ –

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2011年8月20日 · For example, we can say that "20 is evenly divisible by 5", which is equivalent to saying that "5 divides 20"; or in mathematical notation, $5 | 20$. I am sure that the author of the question that you cite, "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?"

2014年11月28日 · "$2$ divides $6$" can be written $2\mid6$. This is a statement and does not have any numerical value. It says that $2$ goes into $6$ exactly with no remainder, or that $6$ is an integer times $2$. This statement is true. Likewise, $3\mid7$ is the statement that $3$ goes into $7$ exactly with no remainder. This statement is false.

2012年8月16日 · The proofs given use the Unique Factorization Theorem, or the existence of GCDs, or some equivalent, but the result is true even in places where there aren't any GCDs, so there must be a proof that doesn't rely on these properties.

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So everything divides 0 right ? that is the opposite of what cited in the question. $\endgroup ...