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Question-127739




Question Number 127739 by Algoritm last updated on 01/Jan/21
Commented by Ndala last updated on 01/Jan/21
y,z∈N  7^z >0⇔2^y −y^6 >0⇔0≤y≤1  f(y)=2^y −y^6 ⇔⇒f(0)=f(1)=1  ⇒7^z =1⇒z=0  S={(1;0);(0;0)}
$${y},{z}\in\mathbb{N} \\ $$$$\mathrm{7}^{{z}} >\mathrm{0}\Leftrightarrow\mathrm{2}^{{y}} −{y}^{\mathrm{6}} >\mathrm{0}\Leftrightarrow\mathrm{0}\leqslant{y}\leqslant\mathrm{1} \\ $$$${f}\left({y}\right)=\mathrm{2}^{{y}} −{y}^{\mathrm{6}} \Leftrightarrow\Rightarrow{f}\left(\mathrm{0}\right)={f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\Rightarrow\mathrm{7}^{{z}} =\mathrm{1}\Rightarrow{z}=\mathrm{0} \\ $$$$\mathrm{S}=\left\{\left(\mathrm{1};\mathrm{0}\right);\left(\mathrm{0};\mathrm{0}\right)\right\} \\ $$

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