Question

How do you find `m` when `mZZ=<-10,8,26>` ? (Abstract algebra)

when `mZZ=<-10,8,26>`

Answer 1

`m=color(red)(18)`

Explanation:

If `mZZ = <...,-10,8,26,...>`
`color(white)("XXXXXXXXXX")`Note
`color(white)("XXXXXXXXXXXX")`I assumed you meant the ordered set to be infinite
`color(white)("XXXXXXXXXXXX")`and not limited to only 3 elements
then `EEk | k in ZZ`
and `< m * (k-1), m * k, m *(k+1 )> = < -10,8,26 >`

[1]`color(white)("XXX")mk-m=-10`
[2]`color(white)("XXX")mk=8`
[3]`color(white)("XXX")mk+m=26`

If we subtract [2] from [3], we get
[4]`color(white)("XXX")m=16`

We can verify this result by substituting `8` for `mk` and `16` for `m` in [1] and getting the required result: `-10`