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## Homework Statement

let a belong to N and x,r belong to Z use the definition of divisibility along with the axioms of Integers to prove that IF 5|a and 15|(2ax+r) then 5|r

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- Thread starter ETuten
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- #1

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let a belong to N and x,r belong to Z use the definition of divisibility along with the axioms of Integers to prove that IF 5|a and 15|(2ax+r) then 5|r

- #2

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How does the definition apply to 5|r? Can you get the form required to show it?

- #3

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It is an if then proof with 5|r being what you are trying to prove.

- #4

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Use the fact that 5|a to substitute.

- #5

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It is an if then proof with 5|r being what you are trying to prove.

Yes of course but you must end up with your next to last step being the defining form of 5|r and the last step being "thus 5|r".

You almost have it. Play with what you have and what you need and see if you can connect the two. I can tell you but the point of you going through the proof is

- #6

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r=15t-2ax=

15t-2(5s)x=

5(3T)-5(2s)x=

5(3t-2sx)=r

since 3t-2sx belongs to Z we have 5|r

does that make sense??

- #7

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r=15t-2ax=

15t-2(5s)x=

5(3T)-5(2s)x=

5(3t-2sx)=r

since 3t-2sx belongs to Z we have 5|r

does that make sense??

Looks good.

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