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Author: Tinku Tara

a-n-N-a-n-1-pour-a-n-3-a-m-1modn-posons-m-n-1-subtituons-cette-valeur-dans-on-a-a-n-1-1modn-Mais-n-n-est-pas-forcement-premier-Test-de-primalite-n-N-n-3-n-2-

Question Number 61096 by Arthur El-bomart last updated on 29/May/19 $$\forall\:{a},\:{n}\:\in\:{N}\::\:\mid{a}−{n}\mid=\mathrm{1}\:{pour}\:{a},\:{n}\:\geqslant\mathrm{3} \\ $$$${a}^{{m}} \equiv\mathrm{1}{modn}\:\left(\ast\right) \\ $$$${posons}\::\:{m}={n}−\mathrm{1}\:\left(\ast'\right) \\ $$$${subtituons}\:{cette}\:{valeur}\:{dans}\:\left(\ast\right). \\ $$$${on}\:{a}:\:{a}^{{n}−\mathrm{1}} \equiv\mathrm{1}{modn}.\:{Mais}\:{n}\:{n}'{est}\:{pas}\:{forcement}\:{premier}. \\ $$$${Test}\:{de}\:{primalite} \\ $$$$\forall\:{n}\:\in\:{N},\:{n}\:\geqslant\mathrm{3}.…

calculus-prove-that-0-1-x-n-1-ln-2-1-x-dx-2-n-k-1-n-H-k-k-

Question Number 126631 by mnjuly1970 last updated on 23/Dec/20 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{calculus}… \\ $$$$\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:::\:\:\:\:\:\:\Omega\overset{??} {=}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}^{{n}−\mathrm{1}} {ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right){dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{2}}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{H}_{{k}}…

if-x-y-z-are-three-distinct-complex-numbers-such-that-x-y-z-y-z-x-z-x-y-0-then-find-the-value-of-x-2-y-z-2-

Question Number 192160 by universe last updated on 10/May/23 $$\mathrm{if}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{are}\:\mathrm{three}\:\mathrm{distinct}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{\mathrm{x}}{\mathrm{y}−{z}}+\frac{\mathrm{y}}{\mathrm{z}−\mathrm{x}}+\frac{\mathrm{z}}{\mathrm{x}−\mathrm{y}}\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\Sigma\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{y}−\mathrm{z}\right)^{\mathrm{2}} } \\ $$ Commented by mehdee42 last updated on 09/May/23…

d-2-y-dx-3-dy-dx-2y-e-4t-y-0-1-y-0-0-solve-with-Laplace-Transform-

Question Number 126620 by fajri last updated on 22/Dec/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}}\:−\:\mathrm{3}\:\frac{{dy}}{{dx}}\:+\:\mathrm{2}{y}\:=\:{e}^{\mathrm{4}{t}} \:,\:{y}\left(\mathrm{0}\right)\:=\:\mathrm{1},\:{y}'\left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$${solve}\:{with}\:{Laplace}\:{Transform}! \\ $$ Answered by Olaf last updated on 22/Dec/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}}…

5-x-7-x-9-8-x-x-

Question Number 126619 by O Predador last updated on 22/Dec/20 $$\: \\ $$$$\:\:\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{7}^{\boldsymbol{\mathrm{x}}} \:=\:\left(\mathrm{9}.\mathrm{8}\right)^{\boldsymbol{\mathrm{x}}} \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\: \\ $$ Answered by…

1-2-2-3-3-4-n-n-1-S-n-

Question Number 126617 by Khalmohmmad last updated on 22/Dec/20 $$\mathrm{1}\centerdot\mathrm{2}+\mathrm{2}\centerdot\mathrm{3}+\mathrm{3}\centerdot\mathrm{4}+…+{n}\left({n}+\mathrm{1}\right) \\ $$$${S}_{{n}} =? \\ $$ Answered by Dwaipayan Shikari last updated on 22/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{{n}}…

Find-1-2-3-2-3-5-2-5-7-2-7-

Question Number 192149 by Shrinava last updated on 09/May/23 $$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{2}^{\mathrm{3}} }\:+\:\frac{\mathrm{5}}{\mathrm{2}^{\mathrm{5}} }\:+\:\frac{\mathrm{7}}{\mathrm{2}^{\mathrm{7}} }\:+\:… \\ $$ Answered by aleks041103 last updated on 09/May/23 $$\underset{{k}=\mathrm{1}}…