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Category: Number Theory

How-many-times-is-digit-0-written-when-listing-all-numbers-from-1-to-3333-

Question Number 18498 by Tinkutara last updated on 22/Jul/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{is}\:\mathrm{digit}\:\mathrm{0}\:\mathrm{written}\:\mathrm{when} \\ $$$$\mathrm{listing}\:\mathrm{all}\:\mathrm{numbers}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{3333}? \\ $$ Commented by richard last updated on 23/Jul/17 $${do}\:{you}\:{want}\:{how}\:{many}\:{zeros}\:{there}\:{are}\:{between}\:\mathrm{1}\:{and}\:\mathrm{3333},\:{or}\:{how}\:{many}\:{times}\:{the}\:“\mathrm{0}''\:{appears},\:{independently}\:{of}\:{the}\:{amount}\:{of}\:{zeros}? \\ $$ Answered…

Let-x-be-the-LCM-of-3-2002-1-and-3-2002-1-Find-the-last-digit-of-x-

Question Number 18135 by Tinkutara last updated on 15/Jul/17 $$\mathrm{Let}\:{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{LCM}\:\mathrm{of}\:\mathrm{3}^{\mathrm{2002}} \:−\:\mathrm{1}\:\mathrm{and} \\ $$$$\mathrm{3}^{\mathrm{2002}} \:+\:\mathrm{1}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:{x}. \\ $$ Commented by mrW1 last updated on 15/Jul/17 $$\mathrm{0} \\…

Let-complex-number-z-a-cos-2a-sin-i-If-z-2-for-any-R-then-the-range-of-real-number-a-is-

Question Number 148951 by EDWIN88 last updated on 01/Aug/21 $${Let}\:{complex}\:{number}\:{z}=\left({a}+\mathrm{cos}\:\theta\right)+\left(\mathrm{2}{a}−\mathrm{sin}\:\theta\right){i}\:. \\ $$$${If}\:\mid{z}\mid\:\leqslant\mathrm{2}\:{for}\:{any}\:\theta\in{R}\:{then}\:{the} \\ $$$${range}\:{of}\:{real}\:{number}\:{a}\:{is}\:\_\_\_ \\ $$ Answered by iloveisrael last updated on 01/Aug/21 Answered by…

solve-log-24sinx-24cosx-3-2-

Question Number 83289 by Cmr 237 last updated on 29/Feb/20 $$\:\:{solve} \\ $$$$\boldsymbol{{log}}_{\left(\mathrm{24}\boldsymbol{{sinx}}\right)} \left(\mathrm{24}\boldsymbol{{cosx}}\right)=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by TANMAY PANACEA last updated on 29/Feb/20 $$\frac{{ln}\mathrm{24}{cosx}}{{ln}\mathrm{24}{sinx}}=\frac{\mathrm{3}}{\mathrm{2}}…

Find-the-integer-closest-to-100-12-143-

Question Number 17446 by Tinkutara last updated on 05/Jul/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{integer}\:\mathrm{closest}\:\mathrm{to} \\ $$$$\mathrm{100}\left(\mathrm{12}\:−\:\sqrt{\mathrm{143}}\right). \\ $$ Commented by ajfour last updated on 06/Jul/17 $$\mathrm{100}\left(\mathrm{12}−\sqrt{\mathrm{143}}\right)=\frac{\mathrm{100}}{\mathrm{12}+\sqrt{\mathrm{143}}} \\ $$$$\:\:\approx\frac{\mathrm{100}}{\mathrm{24}}\:\approx\:\mathrm{4}.\mathrm{2}\: \\…

What-are-next-three-numbers-in-the-following-sequence-4-6-12-18-30-42-60-

Question Number 17303 by RasheedSoomro last updated on 03/Jul/17 $$\mathrm{What}\:\mathrm{are}\:\mathrm{next}\:\mathrm{three}\:\mathrm{numbers} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sequence}: \\ $$$$\mathrm{4},\mathrm{6},\mathrm{12},\mathrm{18},\mathrm{30},\mathrm{42},\mathrm{60},… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Determine-two-distinct-primes-p-and-q-such-that-i-p-q-1-p-q-1-p-q-2-P-All-primes-ii-p-q-1-p-q-1-p-q-2-p-q-2-P-All-primes-

Question Number 17272 by RasheedSoomro last updated on 03/Jul/17 $$\mathrm{Determine}\:\mathrm{two}\:\mathrm{distinct}\:\mathrm{primes}\:\:\:\mathrm{p}\:\:\:\mathrm{and}\:\:\:\mathrm{q}\: \\ $$$$\mathrm{such}\:\mathrm{that}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{p}+\mathrm{q}+\mathrm{1},\mathrm{p}+\mathrm{q}−\mathrm{1},\frac{\mathrm{p}+\mathrm{q}}{\mathrm{2}},\frac{\mathrm{p}−\mathrm{q}}{\mathrm{2}}\:\in\:\mathbb{P}\:\left(\mathrm{All}\:\mathrm{primes}\right)? \\ $$ Commented by prakash jain last updated on…

The-sum-of-the-digits-of-the-number-2-2000-5-2004-is-Will-it-be-13-or-14-

Question Number 17252 by Tinkutara last updated on 02/Jul/17 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{2}^{\mathrm{2000}} \mathrm{5}^{\mathrm{2004}} \:\mathrm{is} \\ $$$$\mathrm{Will}\:\mathrm{it}\:\mathrm{be}\:\mathrm{13}\:\mathrm{or}\:\mathrm{14}? \\ $$ Commented by prakash jain last updated on…