Question Number 194709 by MM42 last updated on 13/Jul/23 $${Show}\:{that}\:\:{in}\:{fibonacci}\:{sequence} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{f}_{\mathrm{3}{n}} ={f}_{{n}} ^{\mathrm{3}} +{f}_{{n}+\mathrm{1}} ^{\mathrm{3}} −{f}_{{n}−\mathrm{1}} ^{\mathrm{3}} \\ $$$$ \\ $$ Answered by TheHoneyCat…
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Question Number 129634 by abdurehime last updated on 17/Jan/21 $$\boldsymbol{{sin}}^{ } \boldsymbol{{x}}+\boldsymbol{{cos}}^{ } \boldsymbol{{x}}=\mathrm{1}\:\mathrm{proof}\:\mathrm{by}\:\mathrm{step}\:\mathrm{by}\:\mathrm{step}\:\mathrm{or}\:\mathrm{by}\:\mathrm{showing}\:\mathrm{all}\:\mathrm{steps}\: \\ $$$$\mathrm{b}/\mathrm{c}\:\mathrm{it}\:\mathrm{is}\:\mathrm{my}\:\mathrm{assignment} \\ $$ Answered by MJS_new last updated on 17/Jan/21…
Question Number 128246 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{suppose}\:{that}\:\:::\:{m}=\frac{\mathrm{4}^{{p}} −\mathrm{1}}{\mathrm{3}}\:,\:\:{where} \\ $$$$\:\:\:\:\:\:\:{p}\:\:{is}\:\:{a}\:{prime}\:{number}\:{and}\:\:{p}>\mathrm{3}. \\ $$$${prove}\:\:{that}\:\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{{m}−\mathrm{1}} \:\overset{{m}} {\equiv}\:\mathrm{1}\:\:\:\:…? \\ $$$$\: \\ $$…
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Question Number 126808 by sdfg last updated on 24/Dec/20 Answered by JMZ last updated on 24/Dec/20 $${Since}\:\phi\:{is}\:{a}\:{homomorphism} \\ $$$$\phi\left({a}+{b}\right)=\phi\left({a}\right)+\phi\left({b}\right). \\ $$$${The}\:{kernel}\:{contais}\:{every}\:{x}\:{which} \\ $$ Answered by…
Question Number 126765 by mnjuly1970 last updated on 24/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{elementary}\:\:{mathematics}… \\ $$$$\:\:\:{if}\:\:\:\:\:\mathrm{13}\:\mid\mathrm{9}^{\mathrm{51}} +{k}+\mathrm{1}\:\:\:,\:{k}\in\mathbb{N} \\ $$$$\:\:\:\:\:\:\:\:{then}\:\:\:{k}_{\left({min}\right)} \:=? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by floor(10²Eta[1])…
Question Number 191731 by Spillover last updated on 29/Apr/23 $$\mathrm{Use}\:\mathrm{laws}\:\mathrm{of}\:\mathrm{algebra}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following} \\ $$$$\left(\mathrm{a}\right)\left[\left(\mathrm{B}−\mathrm{A}\right)\mathrm{u}\left(\mathrm{A}−\mathrm{B}\right)\right]=\left[\left(\mathrm{AuB}\right)−\left(\mathrm{AnB}\right)\right] \\ $$$$\left(\mathrm{b}\right)\mathrm{A}\bigtriangledown\left(\mathrm{AnB}\right)=\mathrm{A}−\mathrm{B} \\ $$ Answered by AST last updated on 29/Apr/23 $$\left({a}\right)\:{B}−{A}={B}\cap{A}^{'} \:\:\:{and}\:\:{A}−{B}={A}\cap{B}^{'}…
Question Number 191501 by normans last updated on 24/Apr/23 $$ \\ $$$$\:\:\:\:{find}\:{a}\:{solution}; \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \:=\:\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right) \\ $$$$ \\ $$ Commented by mehdee42 last…