**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:**

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.