Question Number 186441 by Rupesh123 last updated on 04/Feb/23
Commented by Frix last updated on 04/Feb/23
$${t}=\mathrm{10084} \\ $$$$\mathrm{3}\left({t}^{\mathrm{2}} −\mathrm{4}\right)=\mathrm{17466}^{\mathrm{2}} =\mathrm{305061156} \\ $$
Answered by a.lgnaoui last updated on 04/Feb/23
$${the}\:{probleme}\:{as}\:{Iunderstand} \\ $$$${is}\:{to}\:{fond}\:\boldsymbol{{t}}\:{witch}\:{verified} \\ $$$$\mathrm{10}^{\mathrm{8}} \leqslant\mathrm{3}\left({t}^{\mathrm{2}} \:−\mathrm{4}\right)<\mathrm{10}^{\mathrm{9}} \\ $$$$\:\:\:\:\:\:\:\:\sqrt{\frac{\mathrm{10}^{\mathrm{8}} }{\mathrm{3}}+\mathrm{4}}\leqslant{t}<\sqrt{\frac{\mathrm{10}^{\mathrm{9}} }{\mathrm{3}}+\mathrm{4}}\: \\ $$$${with}\:\boldsymbol{{t}}\:{and}\:\boldsymbol{{n}}\in\mathbb{N}\:\:\: \\ $$$${t}=\mathrm{3}{n}+\mathrm{4}\:\:{t}\:{perfect}\:{squart} \\ $$$${p}^{\mathrm{2}} =\mathrm{3}{n}+\mathrm{4} \\ $$$$ \\ $$