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Question Number 184010 by Rasheed.Sindhi last updated on 01/Jan/23

           determinant (((  determinant (((2023))) )))_( is^  _(a number_(which is divisible_(by_(•_• ) ) ) ) )                (i)its sum of digits                                    &         (ii)its sum of squares of digits

$$\:\:\:\:\:\:\:\:\:\:\underset{\:\underset{\underset{\underset{\underset{\underset{\bullet} {\bullet}} {\boldsymbol{\mathrm{by}}}} {\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{divisible}}}} {\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{number}}}} {\boldsymbol{\mathrm{is}}^{\:} }} {\begin{array}{|c|}{\:\begin{array}{|c|}{\mathrm{2023}}\\\hline\end{array}\:}\\\hline\end{array}} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{digits}} \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\& \\ $$ $$\:\:\:\:\:\:\:\left(\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{squares}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{digits}} \\ $$

Commented byRasheed.Sindhi last updated on 01/Jan/23

★Try to discover some other  properties of  2023.                                 &  ★Try to discover other numbers  which have above property.

$$\bigstar\boldsymbol{\mathcal{T}{ry}}\:\boldsymbol{{to}}\:\boldsymbol{{discover}}\:\boldsymbol{{some}}\:\boldsymbol{{other}} \\ $$ $$\boldsymbol{{properties}}\:\boldsymbol{{of}}\:\:\mathrm{2023}. \\ $$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\& \\ $$ $$\bigstar\boldsymbol{\mathcal{T}{ry}}\:\boldsymbol{{to}}\:\boldsymbol{{discover}}\:\boldsymbol{{other}}\:\boldsymbol{{numbers}} \\ $$ $$\boldsymbol{{which}}\:\boldsymbol{{have}}\:\boldsymbol{{above}}\:\boldsymbol{{property}}. \\ $$

Commented bynikif99 last updated on 02/Jan/23

7^7  mod 7! = 2023. Happy new year.

$$\mathrm{7}^{\mathrm{7}} \:{mod}\:\mathrm{7}!\:=\:\mathrm{2023}.\:{Happy}\:{new}\:{year}. \\ $$

Commented byRasheed.Sindhi last updated on 02/Jan/23

•∩i⊂∈ property sir! Is it your own  discovery?  •HappyNewYear to you too,  sir nikif!

$$\bullet\cap\boldsymbol{\mathrm{i}}\subset\in\:\mathrm{property}\:\mathrm{sir}!\:\mathrm{Is}\:\mathrm{it}\:\mathrm{your}\:\mathrm{own} \\ $$ $$\mathrm{discovery}? \\ $$ $$\bullet\mathrm{HappyNewYear}\:\mathrm{to}\:\mathrm{you}\:\mathrm{too}, \\ $$ $$\boldsymbol{\mathrm{sir}}\:\boldsymbol{\mathrm{nikif}}! \\ $$

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