- #1
Edellaine
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Homework Statement
Show that [tex]2\mathbb{Z} + 5\mathbb{Z} = \mathbb{Z}[/tex]
Homework Equations
where 2Z + 5Z = {a+b | a in 2Z and b in 5Z} = Z
The Attempt at a Solution
For any n in Z, we can write
n= (5-4)n = 5n +(-4)n = 5n + 2(-2n)
And since 5n is in 5Z and 2(-2n) is in 2Z, we can form Z from any combination of elements of 2Z and 5Z.
What they're asking me to prove makes sense intuitively but I'm not sure how to write it. Thanks for the help.
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