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Category: Algebra

10-8-p-9-

Question Number 32780 by fara1990 last updated on 02/Apr/18 $$\mathrm{10}−\mathrm{8}=\frac{{p}}{\mathrm{9}} \\ $$ Answered by Rio Mike last updated on 02/Apr/18 $$\mathrm{2}\:=\:\frac{{p}}{\mathrm{9}} \\ $$$${p}=\mathrm{2}×\mathrm{9} \\ $$$$\mathrm{p}=\mathrm{18}…

a-b-N-gcd-a-b-1-prove-that-a-b-b-a-ab-1-Euler-phi-function-

Question Number 163845 by mnjuly1970 last updated on 12/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\:{a},\:{b}\:\in\:\mathbb{N}\:\:,\:\:{gcd}\left(\:{a}\:,\:\:{b}\:\right)=\mathrm{1} \\ $$$$\:\:\:\:\:{prove}\:\:{that}\: \\ $$$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{a}^{\:\:\varphi\:\left({b}\:\right)} +\:{b}^{\:\varphi\:\left({a}\:\right)} \:\overset{\:{ab}} {\equiv}\:\mathrm{1} \\ $$$$\:\:\:\:\:\varphi\::\:\:\:\mathscr{E}{uler}\:{phi}\:\:{function}\:… \\ $$$$…

For-a-b-c-0-if-a-b-c-n-determine-minimum-and-maximum-values-of-a-2-b-2-c-2-ab-bc-ca-

Question Number 32767 by Rasheed.Sindhi last updated on 01/Apr/18 $$\mathrm{For}\:{a},{b},{c}\geqslant\mathrm{0}\:\mathrm{if}\:{a}+{b}+{c}={n},\:\mathrm{determine} \\ $$$$\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}. \\ $$ Commented by Rasheed.Sindhi last updated on…

Let-a-n-be-a-sequence-such-that-a-1-2-a-n-1-3a-n-4-2a-n-3-n-1-find-a-n-

Question Number 98280 by I want to learn more last updated on 12/Jun/20 $$\boldsymbol{\mathrm{Let}}\:\:\left\{\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \right\}\:\:\boldsymbol{\mathrm{be}}\:\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sequence}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\:\:\boldsymbol{\mathrm{a}}_{\mathrm{1}} \:=\:\:\mathrm{2}, \\ $$$$\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}\:\:+\:\:\mathrm{1}} \:\:=\:\:\frac{\mathrm{3}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:+\:\:\mathrm{4}}{\mathrm{2}\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \:\:+\:\:\mathrm{3}},\:\:\:\:\:\boldsymbol{\mathrm{n}}\:\geqslant\:\mathrm{1},\:\:\:\:\:\boldsymbol{\mathrm{find}}\:\:\:\:\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} \\ $$ Answered by…