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Category: Number Theory

Determine-m-amp-n-such-that-digit-sum-m-2-n-amp-digit-sum-n-2-m-digit-sum-abc-a-b-c-

Question Number 168937 by Rasheed.Sindhi last updated on 21/Apr/22 $$ \\ $$$$\underline{\mathcal{D}{etermine}\:{m}\:\&\:{n}\:{such}\:{that}:} \\ $$$$\:\:\underset{\underset{{digit}-{sum}\left({n}^{\mathrm{2}} \right)={m}} {\&}} {\:{digit}-{sum}\left({m}^{\mathrm{2}} \right)={n}} \\ $$$$\:^{\blacksquare} {digit}-{sum}\left(\overline {{abc}..}.\right)={a}+{b}+{c}+…\:\:\:\:\:\:\:\: \\ $$ Answered…

Find-all-the-values-of-n-such-that-determinant-digit-sum-n-3-n-and-show-that-n-has-at-most-2-digits-digit-sum-abc-a-b-c-

Question Number 168885 by Rasheed.Sindhi last updated on 20/Apr/22 $$ \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}: \\ $$$$\:\:\:\:\begin{array}{|c|}{\mathrm{digit}-\mathrm{sum}\left(\mathrm{n}^{\mathrm{3}} \right)=\mathrm{n}\:}\\\hline\end{array} \\ $$$$\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{n}\:\mathrm{has}\:\mathrm{at}\:\mathrm{most}\:\mathrm{2}\:\mathrm{digits}. \\ $$$$\:\:^{\blacksquare} \mathrm{digit}-\mathrm{sum}\left(\overline {\mathrm{abc}..}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}+… \\ $$…

Q-168480-reposted-n-2-n-109-x-2-x-Z-n-Z-

Question Number 168823 by Rasheed.Sindhi last updated on 18/Apr/22 $$\boldsymbol{\mathrm{Q}}#\mathrm{168480}\:\mathrm{reposted}. \\ $$$$\boldsymbol{\mathrm{n}}^{\mathrm{2}} +\boldsymbol{\mathrm{n}}+\mathrm{109}=\boldsymbol{\mathrm{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{x}}\in\mathbb{Z},\:\boldsymbol{\mathrm{n}}\left(\in\mathbb{Z}^{+} \right)=? \\ $$ Answered by Rasheed.Sindhi last updated on 18/Apr/22…

x-1-x-1-x-1907-1-x-1907-

Question Number 102771 by bramlex last updated on 11/Jul/20 $$\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}\:=\:−\mathrm{1}\:\Rightarrow\mathrm{x}^{\mathrm{1907}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{1907}} }\:?\: \\ $$ Answered by ajfour last updated on 11/Jul/20 $${x}^{\mathrm{2}} +{x}+\mathrm{1}=\mathrm{0} \\ $$$$\Rightarrow\:\:{x}=\omega,\:\omega^{\mathrm{2}}…