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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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