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I remember that problem from my college linear algebra course! I found a nice simple proof for integers (which was very satisfying!) but afaik you do need heavy linear algebra machinery to generalise it to the reals.



> I found a nice simple proof for integers (which was very satisfying!)

But no such proof can exist because the claim is not true. When you posted your comment, Fetiorin had already given a counterexample.


I was pulling the problem from memory. Add the requirement boths sides are same number of items.


Why doesn't the integer proof work on reals?


it relied on modular arithmetic




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