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Category: Number Theory

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}}…

2023-2023-mod-13-

Question Number 201352 by cortano12 last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:=\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 05/Dec/23 $$\:\:\:\mathrm{2023}^{\mathrm{2023}} \:\equiv\:…\:\left(\mathrm{mod}\:\mathrm{13}\right) \\ $$$$\mathrm{2023}^{\mathrm{2023}} \\…

Let-abc-bca-cab-defg-where-a-b-g-are-decimal-digits-may-be-equal-to-0-Show-that-i-dg-a-b-c-ii-e-f-d-g-

Question Number 200836 by Rasheed.Sindhi last updated on 24/Nov/23 $$ \\ $$$$\mathcal{L}{et}\overline {\:{abc}\:}+\overline {\:{bca}\:}+\overline {\:{cab}\:}=\overline {\:{defg}\:} \\ $$$${where}\:{a},{b},…,{g}\:{are}\:{decimal}\:{digits} \\ $$$$\left({may}\:{be}\:{equal}\:{to}\:\mathrm{0}\right)\: \\ $$$${Show}\:{that} \\ $$$$\left({i}\right)\overline {\:{dg}\:}={a}+{b}+{c}…

ab-b-ba-a-cde-ab-b-ba-a-f-a-b-c-d-e-f-are-all-different-and-in-some-order-consecutive-also-Determine-the-remain

Question Number 200315 by Rasheed.Sindhi last updated on 17/Nov/23 $$\:\begin{cases}{\overline {\:{ab}\:}\centerdot\overline {\:{b}\:}+\overline {\:{ba}\:}\centerdot\overline {\:{a}\:}=\overline {\:{cde}\:}}\\{\overline {\:{ab}\:}\centerdot\overline {\:{b}\:}−\overline {\:{ba}\:}\centerdot\overline {\:{a}\:}=\overline {\:{f}\:}\:}\end{cases} \\ $$$${a},{b},{c},{d},{e},{f}\:{are}\:{all}\:{different}\:{and}\:{in} \\ $$$${some}\:{order}\:{consecutive}\:{also}. \\…