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Category: Number Theory

x-is-positive-integer-number-can-you-check-if-Q-x-2-4-x-4-1-3-is-a-natural-number-

Question Number 156419 by cortano last updated on 11/Oct/21 $$\mathrm{x}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{number}\: \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{check}\:\mathrm{if}\:\mathrm{Q}=\sqrt[{\mathrm{3}}]{\left(\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} −\mathrm{x}^{\mathrm{4}} \right.} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{natural}\:\mathrm{number} \\ $$ Commented by mr W last updated on…

What-is-the-real-part-and-imaginary-part-of-the-complex-number-z-1-i-i-

Question Number 25152 by tawa tawa last updated on 05/Dec/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{real}\:\mathrm{part}\:\mathrm{and}\:\mathrm{imaginary}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{number}:\:\:\:\:\mathrm{z}\:=\:\left(\mathrm{1}\:+\:\mathrm{i}\right)^{\mathrm{i}} \\ $$ Commented by tawa tawa last updated on 05/Dec/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered…

A-x-n-x-n-2-x-n-3-x-n-n-1-n-1-n-1-n-1-n-1-n-

Question Number 156201 by VIDDD last updated on 09/Oct/21 $$\:\:{A}=\left[\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}} \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{2}} } \sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{3}} } \centerdot\centerdot\centerdot\centerdot\sqrt[{\mathrm{n}}]{\mathrm{x}^{\mathrm{n}^{\mathrm{n}} } }}}}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$ Commented by talminator2856791 last updated on…

cos-pi-5-with-solution-pls-

Question Number 156126 by VIDDD last updated on 08/Oct/21 $$\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{5}}=…?\:\:\mathrm{with}\:\mathrm{solution}\:\mathrm{pls} \\ $$ Commented by cortano last updated on 08/Oct/21 $$\frac{\pi}{\mathrm{5}}=\mathrm{36}°\:\Rightarrow\mathrm{cos}\:\mathrm{72}°=\mathrm{2cos}\:\mathrm{36}°−\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{36}°=\sqrt{\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{72}°}{\mathrm{2}}}=\sqrt{\frac{\mathrm{1}+\mathrm{sin}\:\mathrm{18}°}{\mathrm{2}}} \\ $$ Answered…

Question-24944

Question Number 24944 by soufiane zarik last updated on 29/Nov/17 Commented by prakash jain last updated on 30/Nov/17 $${x}={n}+{f}\:\:\mathrm{0}\leqslant{f}<\mathrm{1},\:{n}\in\mathbb{Z},{n}\geqslant\mathrm{0} \\ $$$$\left[\left({n}+{f}\right)^{\mathrm{2}} \right]=\left[{n}+{f}\right]^{\mathrm{2}} \\ $$$$\Rightarrow\left[{n}^{\mathrm{2}} +\mathrm{2}{nf}+{f}^{\mathrm{2}}…

Find-the-cube-root-of-one-Hence-show-that-the-sum-of-the-root-is-equal-to-zero-

Question Number 155571 by peter frank last updated on 02/Oct/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\mathrm{one}\:.\mathrm{Hence} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{root}\:\mathrm{is}\: \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{zero} \\ $$ Answered by JDamian last updated on 02/Oct/21 $${z}^{\mathrm{3}}…

A-four-digit-whole-number-is-interesting-if-the-number-formed-by-the-leftmost-two-digits-is-twice-as-large-as-the-number-formed-by-the-rightmost-two-digits-for-example-2010-is-interesting-1-find-t

Question Number 89878 by malwaan last updated on 19/Apr/20 $$\boldsymbol{{A}}\:\boldsymbol{{four\_digit}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{interesting}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{number}} \\ $$$$\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}}\:\boldsymbol{{leftmost}}\:\boldsymbol{{two}} \\ $$$$\boldsymbol{{digits}}\:\boldsymbol{{is}}\:\boldsymbol{{twice}}\:\boldsymbol{{as}}\:\boldsymbol{{large}}\:\boldsymbol{{as}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{number}}\:\boldsymbol{{formed}}\:\boldsymbol{{by}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{rightmost}}\:\boldsymbol{{two}}\:\boldsymbol{{digits}}. \\ $$$$\left(\boldsymbol{{for}}\:\boldsymbol{{example}}\:\mathrm{2010}\:\boldsymbol{{is}}\:\boldsymbol{{interesting}}\right) \\ $$$$\mathrm{1}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{largest}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \\…