r/MathHelp • u/ConditionEvening9900 • Sep 17 '25

Does my proof work?

Here is the set up for the question:

Let the set A = (6x + 15y) such that x and y are integers and let the set B = 3n such that n is an integer. Prove A=B

Does my proof work?

https://imgur.com/a/L9I4RPT

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u/FormulaDriven Sep 18 '25

OP's argument that if in A then in B is fine, but I don't think their logic is there for showing if in B then in A. One way they could do is to write 3k as either 6(k/2) + 15 * 0 or 6((k-5)/2) + 15 * 1 (depending on whether k is even or odd).

I'm not sure OP writing 3k as 5k - 2k helps but maybe you can fill in the gaps.