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

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

1 Answer
Alan P.
Oct 17, 2017

#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#

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