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Partially supported by Universidad Nacional de Rio Cuarto (grant PPI 18/C472) and CONICET (grant PIP 112-201501-00433CO).  Partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria (grant Resol. Nro. 155/14).  Partially supported by Ministerio de Economia, Industria y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT) and by Universidad Nacional del Sur of Argentina (grant 24/L108).

Parametrized solutions $X$ of the system $AXA = AY A$ and $A^k Y AX = XAY A^k$