Question Number 153214 by pticantor last updated on 05/Sep/21
$$\boldsymbol{{let}}\:\boldsymbol{{a}},\boldsymbol{{b}}\in\mathbb{N}^{\ast} \: \\ $$$$\:\boldsymbol{{a}}\ast\boldsymbol{{b}}=\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{ab}} \\ $$$$\boldsymbol{{a}}^{\left(\boldsymbol{{n}}\right)} =\boldsymbol{{a}}^{\left(\boldsymbol{{n}}−\mathrm{1}\right)} \ast\boldsymbol{{a}} \\ $$$$\boldsymbol{{explicite}}\:\boldsymbol{{a}}^{\left(\boldsymbol{{n}}\right)} \:\boldsymbol{{en}}\:\boldsymbol{{fonction}}\:\boldsymbol{{de}}\:\boldsymbol{{a}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by ghimisi last updated on 05/Sep/21
$${a}\ast{b}=\left({a}+\mathrm{1}\right)\left({b}+\mathrm{1}\right)−\mathrm{1} \\ $$$${a}^{\left({n}\right)} =\left({a}+\mathrm{1}\right)^{{n}} −\mathrm{1}\:\:\: \\ $$$$ \\ $$
Commented by pticantor last updated on 05/Sep/21
$${cant}\:{u}\:{explain}\:{please}? \\ $$