noxz-sites

A collection of a builder and various scripts creating the noxz.tech sites
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commit 7af9c83bca436e505783c6cfb5aae0b15f9c837f
parent 6c0949af0918ea9626c2cda1a9c5345d7c336660
Author: Chris Noxz <chris@noxz.tech>
Date:   Tue, 24 Sep 2019 15:38:01 +0200

Be more clear about divisibility theorems

Diffstat:
Mnoxz.tech/guides/mathematics/index.md | 18++++++++++++++++++
1 file changed, 18 insertions(+), 0 deletions(-)

diff --git a/noxz.tech/guides/mathematics/index.md b/noxz.tech/guides/mathematics/index.md @@ -307,6 +307,11 @@ divisible by 3 if, and only if, the sum ..{--} {--} +We have shown that the procedure above will hold for all cases. The procedure +is also recursive. If the sum is to hard to test divisibility for, the +procedure can be repeated, until a smaller sum is reveald. This is rarely +necessary as the divisibility of the sum often is easy to determined. + ### {- id="math-div-theorems-4"}Divisibility by 4{--} The theorem goes that if the last two digits of a number is divisible by 4, the whole number is divisible by 4, i.e. @@ -539,6 +544,14 @@ This theorem is a combination of the theorem for [*divisibility by ..{--} {--} +**Note**: Be careful when combining theroems like this. Don't be fooled and try +to combine divisibility theorems for 2 and 4 to get the theorem for 8, as +numbers divisible by 4 always are divisible by 2. The number 4 is for instance +both divisible by 2 and 4, but **not** by 8. Make sure the theorems you combine +doesn't share a factor, like 4 and 2 sharing the factor 2. It's of course +possible to use theoerems 4 and 2 together, but it's not certain in all cases +that the two theorems prove divisibility by 8. + ### {- id="math-div-theorems-7"}Divisibility by 7{--} Probably one of the most useful theorems is the theorem of *divisibility by 7*, as it is recursive (just like the theorems of *divisibility by 3 & 9*). The @@ -1206,6 +1219,11 @@ divisible by 9 if, and only if, the sum ..{--} {--} +We have shown that the procedure above will hold for all cases. The procedure +is also recursive. If the sum is to hard to test divisibility for, the +procedure can be repeated, until a smaller sum is reveald. This is rarely +necessary as the divisibility of the sum often is easy to determined. + ### {- id="math-div-theorems-10"}Divisibility by 10{--} The theorem goes that if the last digits of a number is divisible by 10, the whole number is divisible by 10, i.e.