Résumé
A long standing question asks whether$\mathbb{Z}$is uniformly 2-repetitive [Justin 1972, Pirillo and Varricchio, 1994], that is, whether there is an infinite sequence over a finite subset of$\mathbb{Z}$avoiding two consecutive blocks of same size and same sum or not. Cassaigne et al. [2014] showed that$\mathbb{Z}$is not uniformly 3-repetitive. We show that$\mathbb{Z}^2$is not uniformly 2-repetitive. Moreover, this problem is related to a question from Mäkelä in combinatorics on words and we answer to a weak version of it.