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What-is-the-remainder-when-x-81-x-49-x-25-x-9-x-is-divided-by-x-3-x-

Question Number 135169 by bramlexs22 last updated on 11/Mar/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\: \\ $$$$\mathrm{x}^{\mathrm{81}} +\mathrm{x}^{\mathrm{49}} +\mathrm{x}^{\mathrm{25}} +\:\mathrm{x}^{\mathrm{9}} +\:\mathrm{x}\:\mathrm{is}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{x}^{\mathrm{3}} +\mathrm{x}\: \\ $$ Terms of Service Privacy…

f-n-1-x-x-f-n-x-g-n-1-x-g-n-x-x-h-n-1-x-h-n-x-h-n-x-f-0-x-g-0-x-h-0-x-x-if-f-x-lim-n-f-n-x-g-x-lim-n-g-n-x-h-x-lim-n-h-n-x-does-f-x-g-x-h-x-

Question Number 4025 by 123456 last updated on 26/Dec/15 $${f}_{{n}+\mathrm{1}} \left({x}\right)={x}^{{f}_{{n}} \left({x}\right)} \\ $$$${g}_{{n}+\mathrm{1}} \left({x}\right)=\left[{g}_{{n}} \left({x}\right)\right]^{{x}} \\ $$$${h}_{{n}+\mathrm{1}} \left({x}\right)=\left[{h}_{{n}} \left({x}\right)\right]^{{h}_{{n}} \left({x}\right)} \\ $$$${f}_{\mathrm{0}} \left({x}\right)={g}_{\mathrm{0}} \left({x}\right)={h}_{\mathrm{0}}…

1-2-2-1-1-2-2-2-2-1-1-2-1-3-2-2-3-1-1-2-1-3-1-4-2-2-4-Find-in-a-closed-form-

Question Number 134984 by Dwaipayan Shikari last updated on 09/Mar/21 $$\frac{\mathrm{1}^{\mathrm{2}} }{\mathrm{2}}+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{3}} }+\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{2}} }{\mathrm{2}^{\mathrm{4}} }+… \\ $$$$ \\ $$Find in a closed…

f-0-R-g-0-R-f-ux-f-uf-x-g-ux-g-u-f-x-f-x-g-x-

Question Number 3886 by 123456 last updated on 23/Dec/15 $${f}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${g}:\left[\mathrm{0},+\infty\right)\rightarrow\mathbb{R} \\ $$$${f}\left({ux}\right)={f}\left({uf}\left({x}\right)\right) \\ $$$${g}\left({ux}\right)={g}\left({u}+{f}\left({x}\right)\right) \\ $$$${f}\left({x}\right)+{g}\left({x}\right)=? \\ $$ Commented by Yozzii last updated…