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Question Number 124705 by ZiYangLee last updated on 05/Dec/20 $$\mathrm{Given}\:\mathrm{that} \\ $$$$\frac{\mathrm{log}\:{a}}{{b}−{c}}=\frac{\mathrm{log}\:{b}}{{c}−{a}}=\frac{\mathrm{log}\:{c}}{{a}−{b}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}^{{a}} {b}^{{b}} {c}^{{c}} . \\ $$ Answered by TANMAY PANACEA last updated…
Question Number 124696 by mathocean1 last updated on 05/Dec/20 $${S}\:\in\:\mathbb{N}. \\ $$$${S}=\left(\mathrm{2}^{\mathrm{0}} ×\mathrm{2}^{\mathrm{1}} ×…×\mathrm{2}^{\mathrm{13}} \right)\left(\mathrm{7}^{\mathrm{0}} ×\mathrm{7}^{\mathrm{1}} ×…×\mathrm{7}^{\mathrm{15}} \right)\left(\mathrm{11}^{\mathrm{0}} ×\mathrm{11}^{\mathrm{1}} ×…×\mathrm{11}^{\mathrm{100}} \right) \\ $$$${determinate}\:{the}\:{sum}\:{of}\:\:{positive} \\ $$$${divisors}\:{of}\:{S}.…
Question Number 124692 by mathocean1 last updated on 05/Dec/20 $${show}\:{that}\:\forall\:{a},{b}\:\in\mathbb{N}^{\ast} , \\ $$$${GCD}\left(\mathrm{13}{a}+\mathrm{8}{b};\mathrm{5}{a}+\mathrm{3}{b}\right)={GCD}\left({a};{b}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124694 by mathocean1 last updated on 05/Dec/20 $${Determinate}\:{m}\:{such}\:{that} \\ $$$${m}\:{is}\:{written}\:{abcca}\:{in}\:{base}\:\mathrm{5}\:{and}\:{is} \\ $$$${written}\:{bbab}\:{in}\:{base}\:\mathrm{8}. \\ $$ Answered by floor(10²Eta[1]) last updated on 05/Dec/20 $$\mathrm{M}=\mathrm{abcca}_{\mathrm{5}} =\mathrm{bbab}_{\mathrm{8}}…
Question Number 124693 by mathocean1 last updated on 05/Dec/20 $${Demonstrate}\:{that}\:\forall\:{a},{b}\:\in\mathbb{N}^{\ast} \:{if}\:\frac{{a}}{{b}} \\ $$$${can}\:{not}\:{be}\:{simplified},\:{then}\:\frac{{a}+{b}}{{a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} } \\ $$$${can}\:{not}\:{also}\:{be}\:{simplified}. \\ $$$$ \\ $$ Answered by MJS_new last…
Question Number 190230 by 073 last updated on 29/Mar/23 Answered by Rasheed.Sindhi last updated on 29/Mar/23 $$\mathrm{a}_{\mathrm{5}} =\mathrm{5}−\mathrm{1}=\mathrm{4}\:\:\:\left[\:\because\:\:\mathrm{5}=\mathrm{2}\left(\mathrm{2}\right)+\mathrm{1}\:\right] \\ $$$$\mathrm{a}_{\mathrm{6}} =\mathrm{2}\left(\mathrm{6}\right)+\mathrm{3}=\mathrm{15}\:\:\:\left[\:\because\:\mathrm{6}=\mathrm{2}\left(\mathrm{3}\right)\:\right] \\ $$$$\mathrm{a}_{\mathrm{5}} +\mathrm{a}_{\mathrm{6}} =\mathrm{4}+\mathrm{15}=\mathrm{19}…
Question Number 124690 by mathocean1 last updated on 05/Dec/20 $${show}\:{that}\:\forall\:{a},{b}\in\mathbb{N}^{\ast} \:{if}\:\delta={GCD}\left({a};{b}\right)\: \\ $$$${then}\:\delta\mathbb{Z}=\left\{{au}+{bv};\:{u}\:{and}\:{v}\:\in\mathbb{Z}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 124688 by mathocean1 last updated on 05/Dec/20 $${Solve}\:{in}\:\mathbb{N}^{\mathrm{2}} : \\ $$$${a}.\:\:\begin{cases}{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} =\mathrm{4704}}\\{{GCD}\left({a};{b}\right)=\mathrm{7}}\end{cases} \\ $$$${b}.\:\:\:\begin{cases}{\mathrm{13}{GCD}\left({a};{b}\right)−\mathrm{2}{SCM}\left({a};{b}\right)=\mathrm{4}}\\{\mathrm{3}<{GCD}\left({a};{b}\right)<\mathrm{7}}\end{cases} \\ $$$$ \\ $$$${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$$${SCM}:\:{smallest}\:{common}\:{multiple} \\ $$…
Question Number 124691 by mathocean1 last updated on 05/Dec/20 $${show}\:{that}\:{the}\:{set}\:{of}\:{prime}\:{numbers} \\ $$$${is}\:{infinite} \\ $$ Answered by MJS_new last updated on 05/Dec/20 $$\mathrm{suppose}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{primes}\:\mathrm{is}\:\mathrm{finite}\:\mathrm{and}\:\mathrm{is}\:{n} \\ $$$$\mathrm{let}\:{N}=\mathrm{1}+\underset{{j}=\mathrm{1}} {\overset{{n}}…