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Category: Number Theory

Prove-that-6-20-1-0-mod-7-

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-206912

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…

x-2-mod-7-x-3-mod-4-x-

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) \\…

how-to-convert-31230-in-base-60-pls-help-

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}}…

abcd-is-a-four-digit-number-such-that-a-2-b-2-c-2-d-2-cd-and-cd-d-ab-Find-the-number-

Question Number 202716 by Rasheed.Sindhi last updated on 01/Jan/24 $$\overline {\:\:{abcd}\:\:}{is}\:{a}\:{four}\:{digit}\:{number} \\ $$$${such}\:{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +{d}^{\mathrm{2}} =\overline {\:{cd}\:} \\ $$$${and}\:\overline {\:{cd}\:}−\overline {\:{d}\:}=\overline {\:{ab}\:}. \\ $$$$\mathcal{F}{ind}\:{the}\:{number}.…

2025-2025-x-mod-17-

Question Number 201418 by cortano12 last updated on 06/Dec/23 $$\:\:\:\:\:\:\mathrm{2025}^{\mathrm{2025}} \:=\:\mathrm{x}\:\left(\mathrm{mod}\:\mathrm{17}\:\right) \\ $$ Answered by mr W last updated on 06/Dec/23 $$\mathrm{2025}^{\mathrm{2025}} \:\left({mod}\:\mathrm{17}\right) \\ $$$$=\left(\mathrm{119}×\mathrm{17}+\mathrm{2}\right)^{\mathrm{2025}}…