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Category: Number Theory

How-many-solution-x-y-z-that-fulfilled-x-y-z-99-x-y-z-N-

Question Number 11321 by Joel576 last updated on 20/Mar/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{solution}\:\left\{{x},\:{y},\:{z}\right\}\:\mathrm{that}\:\mathrm{fulfilled} \\ $$$${x}\:+\:{y}\:+\:{z}\:=\:\mathrm{99}\:? \\ $$$${x},{y},{z}\:\in\:\mathbb{N} \\ $$ Commented by prakash jain last updated on 22/Mar/17 $$\mathrm{Please}\:\mathrm{have}\:\mathrm{a}\:\mathrm{look}\:\mathrm{at}\:\mathrm{stars}\:\mathrm{and}\:\mathrm{bars}…

0-sin-x-0-0-0-sin-2x-0-0-0-sin-3x-0-0-n-th-term-

Question Number 142263 by Dwaipayan Shikari last updated on 28/May/21 $$\begin{pmatrix}{\mathrm{0}\:{sin}\left({x}\right)}\\{\mathrm{0}\:\:\mathrm{0}}\end{pmatrix}!+\begin{pmatrix}{\mathrm{0}\:\:{sin}\left(\mathrm{2}{x}\right)}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}!+\begin{pmatrix}{\mathrm{0}\:\:\:{sin}\left(\mathrm{3}{x}\right)}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}!+…\:{n}^{{th}} \:{term} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-11139

Question Number 11139 by Joel576 last updated on 13/Mar/17 Commented by Joel576 last updated on 13/Mar/17 $$\mathrm{A}\:\mathrm{real}\:\mathrm{number}\:{t},\:\mathrm{so}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{three}−\mathrm{ordered}−\mathrm{pair} \\ $$$$\mathrm{solution}\:\left\{{x},\:{y},\:{z}\right\}\:\mathrm{that}\:\mathrm{fulfilled} \\ $$$${x}^{\mathrm{2}\:} \:+\:\mathrm{2}{y}^{\mathrm{2}} \:=\:\mathrm{3}{z}\:\:\:\mathrm{and}\:\:\:{x}\:+\:{y}\:+\:{z}\:=\:{t} \\ $$$$\mathrm{Find}\:{t}…

Let-n-be-the-smallest-positive-integer-that-is-a-multiple-of-75-and-has-exactly-75-positive-integral-divisors-including-1-and-itself-Find-n-75-

Question Number 11075 by Joel576 last updated on 10/Mar/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{that}\:\mathrm{is} \\ $$$$\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{75}\:\mathrm{and}\:\mathrm{has}\:\mathrm{exactly}\:\mathrm{75}\:\mathrm{positive} \\ $$$$\mathrm{integral}\:\mathrm{divisors},\:\mathrm{including}\:\mathrm{1}\:\mathrm{and}\:\mathrm{itself}. \\ $$$$\mathrm{Find}\:\frac{{n}}{\mathrm{75}} \\ $$ Commented by FilupS last updated on 11/Mar/17…

n-1-5-1-4-n-1-

Question Number 10671 by Saham last updated on 22/Feb/17 $$\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{5}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{n}\:−\:\mathrm{1}} \\ $$ Answered by FilupS last updated on 22/Feb/17 $${S}=\mathrm{5}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{4}^{{n}−\mathrm{1}} }…

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}}…