Question Number 114401 by bemath last updated on 19/Sep/20 $${What}\:{is}\:{reminder}\:{when}\:\mathrm{4}^{\mathrm{29}} \\ $$$${divided}\:{by}\:\mathrm{17} \\ $$ Answered by bobhans last updated on 19/Sep/20 $${because}\:\mathrm{16}\:=\:\mathrm{4}^{\mathrm{2}} \equiv\:−\mathrm{1}\:\left({mod}\:\mathrm{17}\:\right) \\ $$$${we}\:{have}\:\mathrm{4}^{\mathrm{4}}…
find-four-numbers-such-that-the-sum-of-every-two-and-the-sum-of-all-four-should-be-perfect-squaresk-
Question Number 48616 by amankumar last updated on 26/Nov/18 $${find}\:{four}\:{numbers}\:{such}\:{that}\:{the}\:{sum}\:{of}\:{every}\:{two}\:{and}\:{the}\:{sum}\:{of}\:{all}\:{four}\:{should}\:{be}\:{perfect}\:{squaresk}\: \\ $$ Commented by MJS last updated on 26/Nov/18 $${a}\neq{b}\neq{c}\neq{d}? \\ $$$${a},{b},{c},{d}\:\in\mathbb{N}\:\mathrm{or}\:\in\mathbb{Z}?\:\neq\mathrm{0}? \\ $$$$\mathrm{please}\:\mathrm{make}\:\mathrm{it}\:\mathrm{clear} \\…
Question Number 114130 by bemath last updated on 17/Sep/20 Commented by mr W last updated on 17/Sep/20 $${z}=\mathrm{2}: \\ $$$$\overline {{x}\mathrm{2}}×\overline {\mathrm{4}{y}\mathrm{2}}=\mathrm{7344} \\ $$$$\left(\mathrm{10}{x}+\mathrm{2}\right)\left(\mathrm{400}+\mathrm{10}{y}+\mathrm{2}\right)=\mathrm{7344} \\…
Question Number 113221 by frc2crc last updated on 11/Sep/20 $${Does}\:{anyone}\:{know}\:{a}\:{good} \\ $$$${website}\:{for}\:{nested}\:{radicals}? \\ $$$$\sqrt[{\mathrm{6}}]{\mathrm{7}\sqrt[{\mathrm{3}}]{\mathrm{20}}−\mathrm{19}}=\sqrt[{\mathrm{3}}]{\mathrm{5}/\mathrm{3}}−\sqrt[{\mathrm{3}}]{\mathrm{2}/\mathrm{3}} \\ $$ Commented by Dwaipayan Shikari last updated on 11/Sep/20 $$\sqrt{{x}}+\sqrt{{y}}=\sqrt{\mathrm{7}+\sqrt{\mathrm{2}}}…
Question Number 113199 by Rasheed.Sindhi last updated on 11/Sep/20 $${Change}\:{the}\:{following}\:{decimal} \\ $$$${number}\:{into}\:{binary}\:{number}: \\ $$$$\mathrm{73}.\mathrm{108} \\ $$ Commented by bemath last updated on 11/Sep/20 $$\mathrm{what}\:\mathrm{is}\:\mathrm{binary}\:\mathrm{one}\:\mathrm{sir}? \\…
Question Number 113187 by bobhans last updated on 11/Sep/20 $$\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathbb{N}\:\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{a}\sqrt{\mathrm{3}}\:+\mathrm{b}}{\mathrm{b}\sqrt{\mathrm{3}}+\mathrm{c}}\:\in\:\mathrm{Q},\:\mathrm{show} \\ $$$$\mathrm{that}\:\frac{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:\in\:\mathbb{Z} \\ $$ Answered by bemath last updated on 11/Sep/20 $$\mathrm{Fact}\::\:\sqrt{\mathrm{3}}\:\notin\mathrm{Q}\:,\:\mathrm{p}+\mathrm{q}\sqrt{\mathrm{3}}\:\in\mathrm{Q}\:\mathrm{if}\:\mathrm{q}=\mathrm{0}…
Question Number 113134 by bemath last updated on 11/Sep/20 $$\mathrm{any}\:\mathrm{one}\:\mathrm{can}\:\mathrm{explain}\:\mathrm{me}\:\mathrm{how}\:\mathrm{to} \\ $$$$\mathrm{change}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\mathrm{biner}\:\mathrm{number}.\:\mathrm{i}'\mathrm{m}\:\mathrm{forgot}. \\ $$$$\mathrm{example}\:\left(\mathrm{315}\right)_{\mathrm{10}} \:=\:\left(…\right)_{\mathrm{2}} \\ $$$$\mathrm{thank}\:\mathrm{you} \\ $$ Commented by I want…
Question Number 113101 by deArchie last updated on 11/Sep/20 $${Prove}\:{that}\:{GCD}\:\left(\left({a},{b}\right),{b}\right)=\left({a},{b}\right) \\ $$ Commented by MJS_new last updated on 11/Sep/20 $$\mathrm{how}\:\mathrm{do}\:\mathrm{you}\:\mathrm{define}\:\mathrm{the}\:\mathrm{gcd}\:\mathrm{of}\:\mathrm{a}\:\mathrm{number}\:\mathrm{with} \\ $$$$\mathrm{a}\:\mathrm{pair}\:\mathrm{of}\:\mathrm{numbers}?\:\mathrm{check}\:\mathrm{the}\:\mathrm{syntax} \\ $$ Commented…
Question Number 113091 by bobhans last updated on 11/Sep/20 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{the}\:\mathrm{curves} \\ $$$$\mathrm{arg}\left(\mathrm{z}\right)\:=\:\frac{\pi}{\mathrm{3}}\:;\:\mathrm{arg}\left(\mathrm{z}\right)=\:\frac{\mathrm{2}\pi}{\mathrm{3}}\:\mathrm{and}\:\mathrm{arg}\left(\mathrm{z}−\mathrm{2}−\mathrm{2i}\sqrt{\mathrm{3}}\right)=\pi \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{plane}? \\ $$ Answered by john santu last updated on 11/Sep/20 $$\:\left({i}\right)\:{arg}\:\left({z}\right)\:=\:\frac{\pi}{\mathrm{3}}\:\rightarrow\:\frac{{y}}{{x}}\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{3}}\right)…
Question Number 113073 by bobhans last updated on 11/Sep/20 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{n}\:\mathrm{for}\: \\ $$$$\mathrm{which}\:\mathrm{5}^{\mathrm{n}} +\mathrm{1}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7} \\ $$ Answered by john santu last updated on 11/Sep/20 $$\:\:{find}\:{all}\:{positive}\:{integers}\:{n}\:{such} \\…