Progression-free sets in Z_4^n are exponentially small
  We show that for integer $n>0$, any subset $A \subset Z_4^n$ free of three-term arithmetic progressions has size $|A| < 4^{c n}$, with an absolute constant $c \approx 0.926$. 
Ernie Croot, Vsevolod Lev, and Peter Pach
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