Question Number 104038 by bramlex last updated on 19/Jul/20 $${what}\:{is}\:{the}\:{largest}\:{positive} \\ $$$${integer}\:{n}\:{such}\:{that}\:{n}^{\mathrm{3}} +\mathrm{100}\:{is} \\ $$$${divisible}\:{by}\:{n}+\mathrm{10}\:?\: \\ $$ Answered by john santu last updated on 19/Jul/20…
Question Number 169541 by amin96 last updated on 02/May/22 Answered by aleks041103 last updated on 02/May/22 $${That}\:{is}\:{a}\:{repost}\:{to}\:{Q}.\mathrm{161817}\:. \\ $$$${I}'{ve}\:{answered}\:{it}\:{there}. \\ $$ Terms of Service Privacy…
Question Number 38395 by NECx last updated on 25/Jun/18 $${Find}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${z}^{\mathrm{2}} +\mathrm{2}\left(\mathrm{1}+{i}\right){z}\:+\mathrm{2}=\mathrm{0} \\ $$$${leaving}\:{your}\:{answer}\:{in}\:{a}+{ib} \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 103908 by bobhans last updated on 18/Jul/20 $${Find}\:{the}\:{least}\:{positive}\:{integer}\:{n}\:{for} \\ $$$${which}\:{there}\:{exists}\:{a}\:{set}\:\left\{\:{s}_{\mathrm{1}} ,{s}_{\mathrm{2}} ,{s}_{\mathrm{3}} ,…,{s}_{{n}} \:\right\} \\ $$$${consisting}\:{of}\:{n}\:{distinct}\:{positive}\:{integers} \\ $$$${such}\:{that}\:\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{1}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{\mathrm{3}} }\right)…\left(\mathrm{1}−\frac{\mathrm{1}}{{s}_{{n}} }\right) \\…
Question Number 38284 by NECx last updated on 23/Jun/18 $${Find}\:{all}\:{the}\:{complex}\:{number}\:{in}\:{the} \\ $$$${rectangular}\:{form}\:{such}\:{that} \\ $$$$\left({z}−\mathrm{1}\right)^{\mathrm{4}} =−\mathrm{1} \\ $$$$ \\ $$ Commented by MrW3 last updated on…
Question Number 168937 by Rasheed.Sindhi last updated on 21/Apr/22 $$ \\ $$$$\underline{\mathcal{D}{etermine}\:{m}\:\&\:{n}\:{such}\:{that}:} \\ $$$$\:\:\underset{\underset{{digit}-{sum}\left({n}^{\mathrm{2}} \right)={m}} {\&}} {\:{digit}-{sum}\left({m}^{\mathrm{2}} \right)={n}} \\ $$$$\:^{\blacksquare} {digit}-{sum}\left(\overline {{abc}..}.\right)={a}+{b}+{c}+…\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 168885 by Rasheed.Sindhi last updated on 20/Apr/22 $$ \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}: \\ $$$$\:\:\:\:\begin{array}{|c|}{\mathrm{digit}-\mathrm{sum}\left(\mathrm{n}^{\mathrm{3}} \right)=\mathrm{n}\:}\\\hline\end{array} \\ $$$$\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{n}\:\mathrm{has}\:\mathrm{at}\:\mathrm{most}\:\mathrm{2}\:\mathrm{digits}. \\ $$$$\:\:^{\blacksquare} \mathrm{digit}-\mathrm{sum}\left(\overline {\mathrm{abc}..}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}+… \\ $$…
Question Number 168823 by Rasheed.Sindhi last updated on 18/Apr/22 $$\boldsymbol{\mathrm{Q}}#\mathrm{168480}\:\mathrm{reposted}. \\ $$$$\boldsymbol{\mathrm{n}}^{\mathrm{2}} +\boldsymbol{\mathrm{n}}+\mathrm{109}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{x}}\in\mathbb{Z},\:\boldsymbol{\mathrm{n}}\left(\in\mathbb{Z}^{+} \right)=? \\ $$ Answered by Rasheed.Sindhi last updated on 18/Apr/22…
Question Number 103195 by bemath last updated on 13/Jul/20 $$\mathrm{893}{x}\:=\:\mathrm{266}\:\left({mod}\:\mathrm{2432}\right) \\ $$ Commented by Rasheed.Sindhi last updated on 29/Jul/20 $$\Rightarrow\mathrm{47}{x}\equiv\mathrm{14}\left({mod}\:\mathrm{128}\right) \\ $$ Terms of Service…
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