#### Vol. 2, No. 2, 2009

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Roth's theorem in $\mathbb{Z}_4^n$

### Tom Sanders

Vol. 2 (2009), No. 2, 211–234
##### Abstract

We show that if $A\subset {ℤ}_{4}^{n}$ contains no three-term arithmetic progressions in which all the elements are distinct then $|A|=o\left({4}^{n}∕n\right)$.

##### Keywords
Roth–Meshulam, cap set problem, Fourier, Freĭman, Balog–Szemerédi, characteristic 2, $\mathbb Z_4^n$, three-term arithmetic progressions
Primary: 42A05