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Author: Tinku Tara

Question-212531

Question Number 212531 by RojaTaniya last updated on 16/Oct/24 Answered by a.lgnaoui last updated on 17/Oct/24 $$\boldsymbol{\mathrm{x}}=\mathrm{1}+^{\mathrm{7}} \sqrt{\mathrm{2}}\:+\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{3}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}\:}\:\right)^{\mathrm{4}} +\left(^{\mathrm{7}} \sqrt{\mathrm{2}}\:\right)^{\mathrm{5}}…

in-how-many-ways-we-can-distribute-6-distinct-balls-in-3-identical-boxes-

Question Number 212522 by Nadirhashim last updated on 16/Oct/24 $$\:\:\boldsymbol{{in}}\:\boldsymbol{{how}}\:\boldsymbol{{many}}\:\boldsymbol{{ways}}\:\boldsymbol{{we}} \\ $$$$\boldsymbol{{can}}\:\boldsymbol{{distribute}}\:\mathrm{6}\:\boldsymbol{{distinct}} \\ $$$$\boldsymbol{{balls}}\:\boldsymbol{{in}}\:\mathrm{3}\:\boldsymbol{{identical}}\:\boldsymbol{{boxes}} \\ $$ Answered by mehdee7396 last updated on 16/Oct/24 $$\:\mathrm{6}/\mathrm{0}/\mathrm{0}\:{or}\:\mathrm{5}/\mathrm{1}/\mathrm{0}\:{or}\:\mathrm{4}/\mathrm{2}/\mathrm{0}\:\:{or}\:\mathrm{4}/\mathrm{1}/\mathrm{1}\:{or}\:\mathrm{3}/\mathrm{3}/\mathrm{0}/\:{or}\:\mathrm{3}/\mathrm{2}/\mathrm{1}\:{or}\:\mathrm{2}/\mathrm{2}/\mathrm{2} \\…

Question-212518

Question Number 212518 by efronzo1 last updated on 16/Oct/24 $$\:\:\:\cancel{\underbrace{\downharpoonleft}\underline{}\:} \\ $$ Answered by golsendro last updated on 16/Oct/24 $$\:\:\:\cancel{\underline{\underbrace{\pm}} }=\:\left(\mathrm{x}−\mathrm{a}\right)^{\mathrm{2}} +\mathrm{a}\: \\ $$$$\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\:\sqrt{\mathrm{x}−\mathrm{a}}\:+\mathrm{a}\:…

certificate-x-1-x-2n-1-1-and-x-1-x-2n-1-1-All-established-2024-10-16-

Question Number 212519 by MrGaster last updated on 16/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\left({x}−\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} −\mathrm{1}\right)\mathrm{and}\left({x}+\mathrm{1}\right)\mid\left({x}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{1}\right) \\ $$$$\mathrm{All}\:\mathrm{established} \\ $$$$\left[\mathrm{2024}.\mathrm{10}.\mathrm{16}\right] \\ $$ Answered by mathmax last updated…

certificate-x-2n-1-Can-always-be-x-1-be-divisible-

Question Number 212513 by MrGaster last updated on 16/Oct/24 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{certificate}: \\ $$$$\:\:\:\:\:\:\:\:\:{x}^{\mathrm{2}{n}} −\mathrm{1} \\ $$$$\mathrm{Can}\:\mathrm{always}\:\mathrm{be}\:{x}+\mathrm{1}\:\mathrm{be}\:\mathrm{divisible}\:\:\:\:\:\:\:\:\: \\ $$ Answered by A5T last updated on 16/Oct/24 $${x}\equiv−\mathrm{1}\left({mod}\:{x}+\mathrm{1}\right)\Rightarrow{x}^{\mathrm{2}{n}}…

The-numbers-of-pairs-of-natural-numbers-x-y-with-x-y-33-that-satisfy-5-3-x-y-1-2-y-2x-is-A-295-B-296-C-297-D-298-E-299-

Question Number 212515 by efronzo1 last updated on 16/Oct/24 $$\:\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural}\: \\ $$$$\:\:\:\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{with}\:\mathrm{x},\mathrm{y}\:\leqslant\:\mathrm{33}\:\mathrm{that}\: \\ $$$$\:\:\:\mathrm{satisfy}\:\mathrm{5}\:\mid\:\mathrm{3}^{\mathrm{x}^{\mathrm{y}−\mathrm{1}} } \:+\:\mathrm{2}^{\mathrm{y}^{\mathrm{2x}} } \:\mathrm{is}\:…\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\mathrm{295}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{296}\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{297}\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{298}\:\:\:\left(\mathrm{E}\right)\:\mathrm{299} \\ $$ Commented by A5T…