Question Number 208506 by Tawa11 last updated on 17/Jun/24 What is the smallest number which must added to 9454351626 so that it will become divisible…
Question Number 207713 by efronzo1 last updated on 24/May/24 Answered by Berbere last updated on 24/May/24 $$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{x}_{{i}} ^{\mathrm{2}} =\mathrm{125}\Rightarrow{only}\:\mathrm{125}\:{number}\:\neq\mathrm{0}\:{at}\:{least} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{125}} {\sum}}{x}_{{i}}…
Question Number 207436 by CrispyXYZ last updated on 15/May/24 $${a},\:{b}\in\mathbb{N}_{+} ,\:\frac{{b}+\mathrm{1}}{{a}}+\frac{{a}+\mathrm{1}}{{b}}\in\mathbb{Z}.\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\left({a},\:{b}\right)\leqslant\sqrt{{a}+{b}.} \\ $$ Commented by A5T last updated on 15/May/24 $${What}\:{is}\:{meant}\:{by}\:\left({a},{b}\right)? \\ $$…
Question Number 207423 by efronzo1 last updated on 14/May/24 $$\:\:\:\:\downharpoonleft\underline{\:} \\ $$ Answered by mr W last updated on 14/May/24 $${let}\:{a}_{{n}} ={b}_{{n}} +{k} \\ $$$${b}_{{n}+\mathrm{1}}…
Question Number 207060 by efronzo1 last updated on 05/May/24 $$\:\:\downharpoonleft\underline{\:} \\ $$ Commented by mr W last updated on 05/May/24 $${i}\:{think}\:{you}\:{mean}\:{a}_{{n}+\mathrm{2}} . \\ $$ Answered…
Question Number 207021 by efronzo1 last updated on 03/May/24 $$\:\:{If}\:\:{a}_{{n}+\mathrm{1}} =\mathrm{2}−\mathrm{5}{a}_{{n}} \:{and}\:{a}_{\mathrm{4}} =\:−\mathrm{8} \\ $$$$\:\:{prove}\:{that}\:{a}_{\mathrm{43}} −{a}_{\mathrm{30}} \:{divisible}\:{by}\:\mathrm{5} \\ $$ Commented by mr W last updated…
Question Number 206999 by efronzo1 last updated on 03/May/24 $$\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}^{\mathrm{20}} −\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$ Commented by Frix last updated on 03/May/24 $$\mathrm{Prove}\:\mathrm{that}\:{n}^{\mathrm{2}{k}} −\mathrm{1}=\mathrm{0}\left(\mathrm{mod}\left({n}+\mathrm{1}\right)\right): \\ $$$${n}^{\mathrm{2}{k}} −\mathrm{1}=\left({n}+\mathrm{1}\right)\underset{{j}=\mathrm{1}}…
Question Number 206912 by BaliramKumar last updated on 30/Apr/24 Answered by A5T last updated on 30/Apr/24 $${cos}^{\mathrm{2}} \theta+\mathrm{3}\left(\mathrm{1}−{cos}^{\mathrm{2}} \theta\right)+\mathrm{2}=\mathrm{5}−\mathrm{2}{cos}^{\mathrm{2}} \theta \\ $$$$\Rightarrow{Max}=\mathrm{5}−\mathrm{0};\:{Min}=\mathrm{5}−\mathrm{2}\Rightarrow{Difference}=\mathrm{2} \\ $$ Answered…
Question Number 205922 by cortano12 last updated on 03/Apr/24 $$\:\:\:{x}\:=\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right) \\ $$$$\:\:\:{x}=\mathrm{3}\:\left({mod}\:\mathrm{4}\right) \\ $$$$\:\:\:{x}=? \\ $$ Answered by Rasheed.Sindhi last updated on 03/Apr/24 $$\:\:\:{x}\:=\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right)\:\wedge\:{x}=\mathrm{3}\:\left({mod}\:\mathrm{4}\right) \\…
Question Number 204568 by pticantor last updated on 21/Feb/24 $$\boldsymbol{{how}}\:\boldsymbol{{to}}\:\boldsymbol{{convert}}\:\mathrm{31230}\:\boldsymbol{{in}}\:\boldsymbol{{base}}\:\mathrm{60}? \\ $$$$\boldsymbol{{pls}}\:\boldsymbol{{help}} \\ $$ Answered by A5T last updated on 22/Feb/24 $$\mathrm{31230}=\mathrm{520}×\mathrm{60}+\mathrm{30}=\left(\mathrm{8}×\mathrm{60}+\mathrm{40}\right)×\mathrm{60}+\mathrm{30} \\ $$$$=\mathrm{8}×\mathrm{60}^{\mathrm{2}} +\mathrm{40}×\mathrm{60}+\mathrm{30}=\mathrm{8}{eU}_{\mathrm{60}}…