Category: Number Theory

Question Number 21292 by FilupS last updated on 19/Sep/17 $$\mathrm{Let}a,b\in \mathbb{Z}$$$$0<a<b$$$$$$$$\mathrm{How}\mathrm{would}\mathrm{you}\mathrm{find}\mathrm{the}\mathrm{maximum}/$$$$\mathrm{largest}\mathrm{prime}\mathrm{gap}\mathrm{in}(a,b)?$$$$$$$$\mathrm{Note}:$$$$\mathrm{Prime}\:\mathrm{gaps}\:\mathrm{are}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between} \…

Question Number 21053 by tawa tawa last updated on 10/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 86240 by Rio Michael last updated on 27/Mar/20 $$\mathrm{use}\mathrm{the}\mathrm{Chinese}\mathrm{Remainder}\mathrm{theorem}\mathrm{to}\mathrm{find}$$$$x\mathrm{such}\mathrm{that}$$$$x\equiv 2\left(\mathrm{mod}3\right)$$$$2x\equiv 3\left(\mathrm{mod}5\right)$$$$3x\equiv 4\left(\mathrm{mod}7\right)$$ Answered by mr W…

Question Number 85668 by Rio Michael last updated on 23/Mar/20 $$\mathrm{z}=2+\mathrm{i}$$$$\mathrm{find}\arg \left(\mathrm{z}\right)$$ Commented by mathmax by abdo last updated on 24/Mar/20 $$\mid{z}\mid=\sqrt{\mathrm{2}^{\mathrm{2}}…

Question Number 150965 by EDWIN88 last updated on 17/Aug/21 Answered by john_santu last updated on 17/Aug/21 $$\mathrm{R}=\frac{1}{2}\log {}_{10}\mathrm{x}=\frac{1}{2}{\mathrm{P}}^2$$$$\mathrm{S}=\frac{1}{2}\log {}_{10}\mathrm{y}=\frac{1}{2}{\mathrm{Q}}^2$$$$\iff \mathrm{P}+\mathrm{Q}+\mathrm{R}+\mathrm{S}=24$$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}}…