Question Number 62242 by Rasheed.Sindhi last updated on 18/Jun/19 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{180}\:\wedge\:\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{45} \\ $$ Commented by maxmathsup by imad last updated on 19/Jun/19 $$\Delta\left({x},{y}\right)\:=\mathrm{45}\:{and}\:{M}\left({x},{y}\right)=\mathrm{180}\:\Rightarrow{x}\:=\mathrm{45}\:{u}\:\:{and}\:{y}\:=\mathrm{45}\:{v}\:{with}\:\Delta\left({u},{v}\right)=\mathrm{1} \\…
Question Number 62214 by Rasheed.Sindhi last updated on 17/Jun/19 $$\mathrm{Find}\:\mathrm{out}\:\mathrm{x},\mathrm{y}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right)}=\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right)−\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right) \\ $$ Answered by MJS last updated on 17/Jun/19 $$\mathrm{lcm}\:\left({x},\:{y}\right)=\frac{\mathrm{gcd}^{\mathrm{2}} \:\left({x},\:{y}\right)}{\mathrm{gcd}\:\left({x},{y}\right)\:−\mathrm{1}} \\ $$$$\Rightarrow\:\mathrm{gcd}\:\left({x},{y}\right)=\mathrm{2}\wedge\mathrm{lcm}\:\left({x},\:{y}\right)=\mathrm{4}\:\Rightarrow\:…
Question Number 127610 by pticantor last updated on 31/Dec/20 $$\boldsymbol{{Z}}=\mathrm{1}+\left(\mathrm{1}+{i}\right)\boldsymbol{{cos}\theta} \\ $$$$\boldsymbol{{arg}}\left(\boldsymbol{{z}}\right)=? \\ $$ Answered by MJS_new last updated on 31/Dec/20 $$\mathrm{arg}\:\left(\mathrm{1}+\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{cos}\:\theta\right)\:= \\ $$$$=\frac{\pi}{\mathrm{2}}\mathrm{sign}\:\left(\mathrm{cos}\:\theta\right)\:−\mathrm{arctan}\:\frac{\mathrm{1}+\mathrm{cos}\:\theta}{\mathrm{cos}\:\theta} \\…
Question Number 192909 by uchihayahia last updated on 30/May/23 $$\: \\ $$$$\:{let}\:{P}\left({x}\right)\:{is}\:{polinomial}\:{with}\:{integer} \\ $$$$\:{coefficient}\:{s}.{t}\:{P}\left(\mathrm{6}\right){P}\left(\mathrm{38}\right){P}\left(\mathrm{57}\right)+\mathrm{19}\:{is} \\ $$$$\:{divided}\:{by}\:\mathrm{114}.\:{P}\left(-\mathrm{13}\right)=\mathrm{479}\:{and}\:{P}\geqslant\mathrm{0} \\ $$$$\:{what}\:{is}\:{minimum}\:{value}\:{of}\:{P}\left(\mathrm{0}\right)? \\ $$$$ \\ $$ Terms of Service…
Question Number 127111 by benjo_mathlover last updated on 26/Dec/20 $$\:{find}\:{the}\:{value}\:{of}\:{x}\:{such}\:{that}\: \\ $$$$\:\begin{cases}{{x}=\mathrm{2}\:\left({mod}\:\mathrm{5}\right)}\\{{x}=\mathrm{3}\:\left({mod}\:\mathrm{8}\right)\:}\\{{x}=\mathrm{2}\:\left({mod}\:\mathrm{3}\right)}\end{cases} \\ $$ Answered by liberty last updated on 04/Jan/21 $${given}\:\begin{cases}{{x}=\mathrm{2}\:\left({mod}\:\mathrm{5}\right)…\left({i}\right)}\\{{x}=\mathrm{3}\:\left({mod}\:\mathrm{8}\right)…\left({ii}\right)}\\{{x}=\mathrm{2}\:\left({mod}\:\mathrm{3}\right)…\left({iii}\right)}\end{cases} \\ $$$${for}\left({i}\right)\:\Rightarrow\:\mathrm{24}{a}\:\equiv\:\mathrm{2}\:\left({mod}\:\mathrm{5}\right)\: \\…
Question Number 126682 by bramlexs22 last updated on 23/Dec/20 $$\:{Find}\:{the}\:{remainder}\: \\ $$$$\:\mathrm{7}+\mathrm{77}+\mathrm{777}+\mathrm{7777}+…+\underset{\mathrm{2020}\:{times}} {\underbrace{\mathrm{777}…\mathrm{7}}} \\ $$$${when}\:{divided}\:{by}\:\mathrm{9}. \\ $$ Answered by talminator2856791 last updated on 23/Dec/20 $$\:…
Question Number 126677 by AST last updated on 26/Sep/22 Commented by talminator2856791 last updated on 23/Dec/20 $$\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{question}? \\ $$$$\: \\ $$ Commented by talminator2856791 last…
Question Number 126666 by bramlexs22 last updated on 23/Dec/20 $$\:\mathrm{3}+\mathrm{33}+\mathrm{333}+\mathrm{3333}+…+\underset{\mathrm{2020}\:{times}} {\underbrace{\mathrm{3333}…\mathrm{3}}}\: \\ $$$${divide}\:{by}\:\mathrm{2}.\:{find}\:{the}\:{remainder} \\ $$ Answered by JDamian last updated on 23/Dec/20 $${it}\:{is}\:{easy} \\ $$$$\mathrm{0}…
Question Number 126657 by adeyemiprof40 last updated on 23/Dec/20 Answered by Olaf last updated on 23/Dec/20 $${a}^{\mathrm{4}} +{a}^{\mathrm{3}} +{a}^{\mathrm{2}} +{a}+\mathrm{1}\:=\:\mathrm{0} \\ $$$$\Leftrightarrow\:\frac{{a}^{\mathrm{5}} −\mathrm{1}}{{a}−\mathrm{1}}\:=\:\mathrm{0},\:{a}\neq\mathrm{1} \\ $$$$\Leftrightarrow\:{a}^{\mathrm{5}}…
Question Number 191889 by cortano12 last updated on 03/May/23 $$\:\:\:\:\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{k}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2n}}\:=? \\ $$ Answered by mahdipoor last updated on 03/May/23 $$\underset{{n}=\mathrm{1}} {\overset{{k}} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}}…