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Category: Arithmetic

Question-138320

Question Number 138320 by aliibrahim1 last updated on 12/Apr/21 Answered by Rasheed.Sindhi last updated on 17/Apr/21 $$\mathrm{11}^{{n}} =\left(\mathrm{1}+\mathrm{10}\right)^{{n}} =\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\left(\mathrm{10}\right)^{\mathrm{0}} +\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\left(\mathrm{10}\right)^{\mathrm{1}} \\ $$$$\:\:\:\:\:\:\:+\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\left(\mathrm{10}\right)^{\mathrm{2}} +\underset{{divisible}\:{by}\:\mathrm{1000}} {\underbrace{\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\left(\mathrm{10}\right)^{\mathrm{3}} ….+\begin{pmatrix}{{n}}\\{{n}}\end{pmatrix}\left(\mathrm{10}\right)^{{n}}…

Question-7246

Question Number 7246 by Tawakalitu. last updated on 18/Aug/16 Answered by Yozzia last updated on 19/Aug/16 $${Define}\:{the}\:{number}\:{k}\:{such}\:{that}\: \\ $$$${k}={x}^{{n}+\mathrm{3}} +{y}^{{n}+\mathrm{3}} +{z}^{{n}+\mathrm{3}} −{xyz}\left({x}^{{n}} +{y}^{{n}} +{z}^{{n}} \right)…

Question-7163

Question Number 7163 by Tawakalitu. last updated on 14/Aug/16 Commented by sou1618 last updated on 14/Aug/16 $$\underset{{a}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}\left(\underset{{b}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}{a}^{{b}} \right)=\underset{{a}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}\left({a}^{\mathrm{0}} +{a}^{\mathrm{1}}…