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Category: Algebra

if-g-5-f-5-g-5-f-5-1-then-f-4-g-4-f-4-1-when-is-Gis-a-I-function-and-F-is-a-constant-

Question Number 161666 by mathlove last updated on 21/Dec/21 $${if}\:\:\frac{{g}\left(\mathrm{5}\right){f}\left(\mathrm{5}\right)}{{g}\left(\mathrm{5}\right)+{f}\left(\mathrm{5}\right)}=\mathrm{1}\:\:\:{then}\frac{{f}\left(\mathrm{4}\right)+{g}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)+\mathrm{1}}=? \\ $$$${when}\:{is}\:\:\:\:\:{Gis}\:{a}\:{I}\:{function}\:\:{and}\:{F}\:{is}\:{a}\:{constant} \\ $$ Commented by mr W last updated on 21/Dec/21 $${the}\:{language}\:{is}\:{not}\:{clear}. \\ $$$${what}\:{are}\:{G}\:{and}\:{F}?…

n-k-1-k-n-is-a-family-of-integrs-numbers-let-put-p-x-k-1-n-x-n-k-and-q-x-j-0-n-1-x-j-if-n-k-k-1-n-prove-that-q-divide-p-

Question Number 30588 by abdo imad last updated on 23/Feb/18 $$\left({n}_{{k}} \right)_{\mathrm{1}\leqslant{k}\leqslant{n}} \:{is}\:{a}\:{family}\:{of}\:{integrs}\:{numbers}\:{let}\:{put} \\ $$$${p}\left({x}\right)=\sum_{{k}=\mathrm{1}} ^{{n}} \:{x}^{{n}_{{k}} } \:\:\:{and}\:{q}\left({x}\right)=\:\sum_{{j}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{x}^{{j}} \: \\ $$$${if}\:{n}_{{k}} \equiv{k}−\mathrm{1}\left[{n}\right]\:{prove}\:{that}\:{q}\:{divide}\:{p}.…

x-1-x-2-x-3-are-roots-of-the-polynomial-x-3-x-1-find-the-polynomial-wich-have-for-roots-x-1-3-x-2-3-and-x-3-3-

Question Number 30582 by abdo imad last updated on 23/Feb/18 $${x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}\:} \:{are}\:{roots}\:{of}\:{the}\:{polynomial}\:{x}^{\mathrm{3}} \:−{x}+\mathrm{1}\:{find} \\ $$$${the}\:{polynomial}\:{wich}\:{have}\:{for}\:{roots}\:{x}_{\mathrm{1}} ^{\mathrm{3}} \:,{x}_{\mathrm{2}} ^{\mathrm{3}} \:{and}\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:\:. \\ $$…