= Roth theorem on three-term arithmetic progressions
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= Roth theorem for arithmetic progressions
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For every $\delta>0$, every sufficiently long integer interval has a nonconstant three-term <arithmetic progression> in each subset of <subset density> at least $\delta$. This is a theorem about <additive combinatorics>, distinct from the <Roth theorem> on approximation of algebraic irrational numbers. The <Roth density-increment step> proves it by repeatedly increasing <subset density> on a shorter <arithmetic progression>.
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