Question Number 9025 by Rasheed Soomro last updated on 15/Nov/16 $$\mathrm{Determine}\:\mathrm{number}/\mathrm{s}\:\mathrm{that}\:\mathrm{is}/\mathrm{are}\:\mathrm{comprised} \\ $$$$\mathrm{of}\:\mathrm{four}\:\mathrm{distinct}\:\mathrm{prime}\:\mathrm{factors}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{difference}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{and}\:\mathrm{smallest}\:\mathrm{prime} \\ $$$$\mathrm{factors}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{remaining} \\ $$$$\mathrm{two}\:\mathrm{factors}.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:_{\mathrm{Propsed}\:\mathrm{by}\:\mathrm{Rasheed}\:\mathrm{Soomro}} \\ $$ Commented by FilupSmith last…
Question Number 9021 by tawakalitu last updated on 14/Nov/16 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\: \\ $$$$\left(\mathrm{13}^{\mathrm{5}} \:+\:\mathrm{14}^{\mathrm{5}} \:+\:\mathrm{15}^{\mathrm{5}} \:+\:\mathrm{16}^{\mathrm{5}} \right)\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{29}\:?\: \\ $$ Answered by aydnmustafa1976 last updated on 14/Nov/16…
Question Number 8838 by tawakalitu last updated on 31/Oct/16 $$\mathrm{Show}\:\mathrm{that}\::\:\:\mathrm{e}^{\mathrm{i}\pi\:+\:\mathrm{1}} \:=\:\mathrm{0} \\ $$ Answered by FilupSmith last updated on 31/Oct/16 $$\mathrm{do}\:\mathrm{you}\:\mathrm{mean}\:{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$$${e}^{{ix}} =\mathrm{cos}\left({x}\right)+{i}\mathrm{sin}\left({x}\right)…
Question Number 139668 by aupo14 last updated on 30/Apr/21 Commented by mr W last updated on 30/Apr/21 $${x}^{\mathrm{2}} \:{can}\:{only}\:{be}\:{formed}\:{from}\:{two}\:{times}\: \\ $$$$\left(\mathrm{1}+{x}+{x}^{\mathrm{3}} \right).\:{therefore}\:{the}\:{coefficient} \\ $$$${of}\:{x}^{\mathrm{2}} \:{is}\:{C}_{\mathrm{2}}…
Question Number 139560 by Dwaipayan Shikari last updated on 28/Apr/21 $$\underset{{n}_{\mathrm{1}} +\mathrm{2}{n}_{\mathrm{2}} +\mathrm{3}{n}_{\mathrm{3}} +..+{rn}_{{r}} ={n}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}_{\mathrm{1}} !{n}_{\mathrm{2}} !{n}_{\mathrm{3}} !..{n}_{{r}} !\mathrm{1}^{{n}_{\mathrm{1}} } \mathrm{2}^{{n}_{\mathrm{2}} } \mathrm{3}^{{n}_{\mathrm{3}}…
Question Number 8347 by sou1618 last updated on 09/Oct/16 $${a}_{\mathrm{1}} =\mathrm{2}\:,\:\:{a}_{{n}+\mathrm{1}} >{a}_{{n}} \\ $$$$\left({a}_{{n}+\mathrm{1}} −{a}_{{n}} \right)^{\mathrm{2}} =\:\mathrm{2}\left({a}_{{n}+\mathrm{1}} +{a}_{{n}} \right) \\ $$$$\:{a}_{{n}} =?? \\ $$$${help}\:{me}\:{please}. \\…
Question Number 8336 by Rasheed Soomro last updated on 08/Oct/16 $$\mathrm{Determine}\:\mathrm{smallest}\:\mathrm{n}\left(\neq\mathrm{0}\right),\:\mathrm{for}\:\mathrm{which} \\ $$$$\left(\omega+\mathrm{i}\right)^{\mathrm{n}} =\mathrm{1}. \\ $$ Commented by prakash jain last updated on 08/Oct/16 $${w}=\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{3}}+{i}\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{3}}=−\frac{\mathrm{1}}{\mathrm{2}}+{i}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}…
Question Number 8302 by tawakalitu last updated on 07/Oct/16 $$\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{satisfying}\: \\ $$$$\mathrm{1}!\:+\:\mathrm{2}!\:+\:\mathrm{3}!\:+\:…\:+\:\mathrm{x}!\:=\:\mathrm{y}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8174 by prakash jain last updated on 02/Oct/16 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{infinite}\:\mathrm{prime} \\ $$$$\mathrm{numbers}\:\mathrm{of}\:\mathrm{the}\:\mathrm{form}\:\mathrm{10}^{{n}} +\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 8139 by sou1618 last updated on 01/Oct/16 $${is}\:{it}\:{correct}? \\ $$$${when} \\ $$$${S}_{{n}} =\left\{\right. \\ $$$$\mathrm{1}×\mathrm{2}+\mathrm{1}×\mathrm{3}+\mathrm{1}×\mathrm{4}+\mathrm{1}×\mathrm{5}+…….+\mathrm{1}×{n} \\ $$$$\:\:\:\:\:\:\:\:\:\:+\mathrm{2}×\mathrm{3}+\mathrm{2}×\mathrm{4}+\mathrm{2}×\mathrm{5}+…….+\mathrm{2}×{n} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{3}×\mathrm{4}+\mathrm{3}×\mathrm{5}+…….+\mathrm{3}×{n} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{4}×\mathrm{5}+…….+\mathrm{4}×{n} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….…