The subject of divides encompasses a wide range of important elements. What does it mean to say "a divides b" - Mathematics Stack Exchange. That's the source of your confusion. "a|b" is shorthand for "a divides evenly into b with no remainder" whereas "a/b" is the result you get when you divide b into a.
What does "$x$ divides $y$" mean? - Mathematics Stack Exchange. 2 x divides y means there exists an integer n such that nx=y. So 7 divides 28, since 4*7=28, but 8 does not divide 28, even though outside number theory we would happily deal with the number 3.5. Is $b\mid a$ standard notation for $b$ divides $a$?
This is the standard way, in the specific meaning of compliance to international standards: ISO 80000-2, clause 2.7-17. Moreover, 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 ... algebra precalculus - Understanding "Divides" aka "|" as used logic .... 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"? What is meant by "evenly divisible"? This perspective suggests that, "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible? Equally important, proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\\binom pk$.
Since in the numerator we have k consecutive integers, k divides one of them (not p as p is prime and $k <p$). Then k-1 divides another one or two terms in the k consecutive terms (again not p). Vertical bar sign in Discrete mathematics.
In number theory the sign $\mid$ denotes divisibility. But you need to carefully note that this is definitely not the same as division. "$2$ divided by $6$" can be written $2/6$ or $2\div6$. Its value is one third, or $0.333\ldots\,$.
"$2$ 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 ... Proof of Euclid's Lemma - Mathematics Stack Exchange.
I saw on the internet the following Proof of Euclid's lemma, which states that if a prime number divides the product of two numbers, then it must divide at least one of the two numbers. Suppose that $a$ and $b$ are natural numbers such that $a^2 = b^3 ....
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