(u₁u₂ ⋅⋅⋅ u_n)² = u₁²u₂² ⋅⋅⋅ u_n²,

(u₁u₂ ⋅⋅⋅ u_n)³ = u₁³u₂³⋅⋅⋅ u_n³

hold simultaneously and the words u_i, i = 1, ..., n, do not pairwise commute (that is, u_iu_j ≠ u_ju_i for at least one pair of indices i,j∈{1,2,...,n })?

For the solution an award of 200€ (100 € upped during WORDS 2011 in Prague) is promised. Details here.

Recently, the problem has been solved by Aleksi Saarela.

-- StepanHolub - 01 Aug 2011