Question Number 21229 by Tinkutara last updated on 16/Sep/17 $$\mathrm{Let}\:{p},\:{q}\:\mathrm{be}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$${n}^{\mathrm{3}{pq}} \:−\:{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}{pq}\:\mathrm{for}\:\boldsymbol{\mathrm{all}} \\ $$$$\mathrm{positive}\:\mathrm{integers}\:{n}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:{p}\:+\:{q}. \\ $$ Terms of Service Privacy Policy Contact:…
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Question Number 21031 by youssoufab last updated on 10/Sep/17 $${if}\::\forall\epsilon>\mathrm{0},\:\forall\left({a},{b}\right)\in\mathbb{R}^{\mathrm{2}} ,{a}<{b}+\epsilon \\ $$$${prove}:\:{a}\leqslant{b} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86240 by Rio Michael last updated on 27/Mar/20 $$\mathrm{use}\:\mathrm{the}\:\mathrm{Chinese}\:\mathrm{Remainder}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{find} \\ $$$$\:\:{x}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}\:\equiv\:\mathrm{2}\left(\mathrm{mod}\:\mathrm{3}\right) \\ $$$$\mathrm{2}{x}\:\equiv\:\mathrm{3}\left(\mathrm{mod}\:\mathrm{5}\right) \\ $$$$\:\mathrm{3}{x}\equiv\:\mathrm{4}\left(\:\mathrm{mod}\:\mathrm{7}\right) \\ $$ Answered by mr W…
Question Number 151265 by liberty last updated on 19/Aug/21 Commented by Tawa11 last updated on 19/Aug/21 $$\mathrm{Weldone}\:\mathrm{sir}. \\ $$ Commented by liberty last updated on…
Question Number 85668 by Rio Michael last updated on 23/Mar/20 $$\mathrm{z}\:=\:\mathrm{2}\:+\:\mathrm{i}\: \\ $$$$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right) \\ $$ Commented by mathmax by abdo last updated on 24/Mar/20 $$\mid{z}\mid=\sqrt{\mathrm{2}^{\mathrm{2}}…
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Question Number 150965 by EDWIN88 last updated on 17/Aug/21 Answered by john_santu last updated on 17/Aug/21 $$\mathrm{R}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}} \\ $$$$\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:_{\mathrm{10}} \mathrm{y}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{Q}^{\mathrm{2}} \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\mathrm{R}+\mathrm{S}\:=\:\mathrm{24}\: \\ $$$$\Leftrightarrow\mathrm{P}+\mathrm{Q}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{P}^{\mathrm{2}}…
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Question Number 85261 by Umar last updated on 20/Mar/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{1}+\sqrt{−\mathrm{3}}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} \\ $$$$ \\ $$$$\mathrm{help}\:\mathrm{please} \\ $$ Commented by mathmax by abdo last updated on 20/Mar/20…