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Category: Number Theory

determine-if-1-2-s-1-3-s-1-5-s-1-1-s-1-4-s-1-6-s-or-n-P-n-1-1-n-s-n-P-n-1-1-n-s-Re-s-gt-1-note-n-P-n-1-1-n-s-n-P-n-

Question Number 10662 by FilupS last updated on 22/Feb/17 $$\mathrm{determine}\:\mathrm{if}: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{s}} }+\frac{\mathrm{1}}{\mathrm{3}^{{s}} }+\frac{\mathrm{1}}{\mathrm{5}^{{s}} }+…\geqslant\frac{\mathrm{1}}{\mathrm{1}^{{s}} }+\frac{\mathrm{1}}{\mathrm{4}^{{s}} }+\frac{\mathrm{1}}{\mathrm{6}^{{s}} }+… \\ $$$$\mathrm{or}: \\ $$$$\underset{\underset{{n}\geqslant\mathrm{1}} {{n}\in\mathbb{P}}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{s}}…

log-5-1-10-9e-2-2-1-2-9-2-10-2-3-3-1-3-9-3-10-3-4-4-1-4-9-4-10-4-Euler-Mascheroni-Constant-

Question Number 141694 by Dwaipayan Shikari last updated on 22/May/21 $${log}\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{10}}\mathrm{9}{e}^{\gamma} \right)=\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}}\left(\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} }{\mathrm{10}^{\mathrm{2}} }\right)−\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{3}}\:\left(\frac{\mathrm{1}^{\mathrm{3}} +\mathrm{9}^{\mathrm{3}} }{\mathrm{10}^{\mathrm{3}} }\:\right)+\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{4}}\left(\frac{\mathrm{1}^{\mathrm{4}} +\mathrm{9}^{\mathrm{4}} }{\mathrm{10}^{\mathrm{4}} }\right)−… \\ $$$$\gamma={Euler}\:{Mascheroni}\:{Constant} \\ $$…

Question-75987

Question Number 75987 by Ajao yinka last updated on 21/Dec/19 Answered by MJS last updated on 22/Dec/19 $${m}=\sqrt{{x}}\wedge{n}=\sqrt{{y}} \\ $$$${x}^{\mathrm{3}} +\left(\mathrm{375}{y}\right){x}+\left({y}^{\mathrm{3}} −\mathrm{1953125}\right)=\mathrm{0} \\ $$$$\mathrm{Cardano}\:\mathrm{with}\:{p}=\mathrm{375}{y}\wedge{q}={y}^{\mathrm{3}} −\mathrm{1953125}…

1-2-3-4-5-6-7-8-9-10-11-x-y-The-sum-of-all-possible-solutions-of-x-and-y-is-

Question Number 10364 by Joel575 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}\:=\:{x}^{{y}} \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{is}\:… \\ $$ Answered by mrW1 last updated on 05/Feb/17 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}=\frac{\mathrm{11}×\mathrm{12}}{\mathrm{2}}=\mathrm{66} \\ $$$${x}^{{y}} =\mathrm{66}…