Question Number 39799 by tapukumar056@gmail.com last updated on 11/Jul/18 $$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{will}}\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{makes}}\:\mathrm{680621} \\ $$$$\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{perfect}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{root}}? \\ $$ Answered by $@ty@m last updated on 11/Jul/18 $$\mathrm{8}\mid\mathrm{680621}\mid\mathrm{825} \\ $$$$\mathrm{8}\mid\mathrm{64} \\…
Question Number 39708 by NECx last updated on 10/Jul/18 $${Find}\:{the}\:{complex}\:{number}\:{z}\:{if} \\ $$$${arg}\left({z}+\mathrm{1}\right)=\frac{\pi}{\mathrm{3}} \\ $$$${arg}\left({z}−\mathrm{1}\right)=\frac{\mathrm{4}\pi}{\mathrm{3}} \\ $$ Answered by MrW3 last updated on 10/Jul/18 $${let}\:{z}={a}+{bi} \\…
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Question Number 170046 by Rasheed.Sindhi last updated on 14/May/22 $$\mathrm{PROVE}\:\mathrm{THAT} \\ $$$$\:\:\:\:\mathrm{6}\:\mid\:\left(\mathrm{8}^{{x}} −\mathrm{2}^{{x}} \right) \\ $$ Answered by JDamian last updated on 14/May/22 $$\left(\mathrm{8}^{{x}} −\mathrm{2}^{{x}}…
Question Number 170003 by mathlove last updated on 13/May/22 $${prove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$ Commented by mathlove last updated on…
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Question Number 104139 by bobhans last updated on 19/Jul/20 $${what}\:{is}\:{remainder}\:{when}\:\mathrm{61}^{\mathrm{61}} \:{divided} \\ $$$${by}\:\mathrm{1001} \\ $$ Commented by aurpeyz last updated on 19/Jul/20 $$\mathrm{how}? \\ $$…
Question Number 104100 by bramlex last updated on 19/Jul/20 $$\left(\mathrm{1}\right)\mathbb{F}{ind}\:{all}\:{natural}\:{pairs}\:{of} \\ $$$${integers}\:\left({x},{y}\right)\:{such}\:{that}\:{x}^{\mathrm{3}} −{y}^{\mathrm{3}} ={xy}+\mathrm{61}. \\ $$$$\left(\mathrm{2}\right)\mathbb{F}{ind}\:{gcd}\left({x}^{\mathrm{4}} −{x}^{\mathrm{3}} ,\:{x}^{\mathrm{3}} −{x}\right)\: \\ $$ Answered by bemath last…
Question Number 104093 by bramlex last updated on 19/Jul/20 $$\left(\mathrm{1}\right){Evaluate}\:{the}\:{sum}\:\lfloor\frac{\mathrm{2}^{\mathrm{0}} }{\mathrm{3}}\rfloor+\lfloor\frac{\mathrm{2}^{\mathrm{1}} }{\mathrm{3}}\rfloor+\lfloor\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}}\rfloor+…+\lfloor\frac{\mathrm{2}^{\mathrm{1000}} }{\mathrm{3}}\rfloor \\ $$$$\left(\mathrm{2}\right)\:{find}\:\mathrm{2}^{\mathrm{98}} \:\left({mod}\:\mathrm{33}\right)\: \\ $$ Answered by JDamian last updated on…