# Transfinite arithmetic --- Introduction ---

This is an exercise as well as a game. Let a set $E$ of $k$ elements in the finite ring $ℤ/nℤ$, represented by $k$ integers between 0 and $n-1$. For any element $t\in ℤ/nℤ$, the addition or multiplication by $t$ transforms $E$ into another set ${E}_{t}\subset ℤ/nℤ$.

Thus the exercise generates two sets $E$,$F\subset ℤ/nℤ$, of the same number of elements, and asks you to transform $E$ into $F$ by successive additions and multiplications by elements of $ℤ/nℤ$. And you will be scored according to the number of steps you make.

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• Description: transformation in Z/nZ by addition and multiplication. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
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