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A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.

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Odd partition with extra properties

Multiply by the least common multiple $M$ of the denominators to get the equivalent problem: The $a_i$ are positive integers. $k$ is an odd number. We can partition $A$ into two parts of equal sum. I …
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