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Category: Number Theory

Find-the-units-digit-of-2013-1-2013-2-2013-3-2013-2013-

Question Number 117369 by bemath last updated on 11/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2013}^{\mathrm{1}} +\mathrm{2013}^{\mathrm{2}} +\mathrm{2013}^{\mathrm{3}} +…+\mathrm{2013}^{\mathrm{2013}} \\ $$ Answered by JDamian last updated on 11/Oct/20 $${S}=\mathrm{2013}^{\mathrm{1}} +\mathrm{2013}^{\mathrm{2}} +\:\centerdot\centerdot\centerdot\:+\:\mathrm{2013}^{\mathrm{2013}}…

If-x-is-a-complex-number-satisfying-x-2-x-1-0-what-is-the-value-of-x-53-x-52-x-51-x-50-x-49-

Question Number 117045 by bobhans last updated on 09/Oct/20 $$\mathrm{If}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{satisfying}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\:=\:\mathrm{0}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{53}} +\mathrm{x}^{\mathrm{52}} +\mathrm{x}^{\mathrm{51}} +\mathrm{x}^{\mathrm{50}} +\mathrm{x}^{\mathrm{49}} \:? \\ $$ Answered by john…

739-is-a-prime-number-and-its-reversed-number-937-is-also-prime-Determine-4-digit-prime-numbers-whose-reversed-be-also-prime-If-number-of-such-primes-is-a-function-of-number-of-digits-determ

Question Number 51507 by Rasheed.Sindhi last updated on 27/Dec/18 $$\:^{\bullet} \mathrm{739}\:{is}\:{a}\:\:{prime}\:{number}\:{and} \\ $$$${its}\:{reversed}\:{number}\:\mathrm{937}\:{is}\:{also} \\ $$$${prime}. \\ $$$${Determine}\:\mathrm{4}-{digit}\:{prime}\:{numbers} \\ $$$${whose}\:{reversed}\:{be}\:{also}\:{prime}. \\ $$$$\:^{\bullet} {If}\:{number}\:{of}\:{such}\:{primes}\:{is}\:{a} \\ $$$${function}\:{of}\:{number}\:{of}\:{digits}, \\…

Let-S-1-2-3-4-5-6-7-If-we-multiply-atleast-2-numbers-from-this-set-with-each-other-what-are-the-chances-of-the-product-to-turn-out-to-be-divisible-by-3-

Question Number 182199 by depressiveshrek last updated on 05/Dec/22 $${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$ Answered by Acem last updated…

4-3-2-5-3-1-1-6-1-2-8-1-find-numbers-of-each-

Question Number 50960 by kaivan.ahmadi last updated on 22/Dec/18 $$\mathrm{4}\:\:\:\left(\mathrm{3}\right)\:\:\:\:\mathrm{2} \\ $$$$\mathrm{5}\:\:\:\:\mathrm{3}\:\:\:\left(?\right)\:\:\mathrm{1}\:\:\:\:\mathrm{1} \\ $$$$\mathrm{6}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\left(\mathrm{8}\right)\:\:\:\:?\:\:\:\:\:?\:\:\:\:\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{each}\:\:\:? \\ $$ Terms of Service Privacy Policy…

Let-S-1-2-3-4-48-49-What-is-the-maximum-value-of-n-such-that-it-is-possible-to-select-n-numbers-from-S-and-arrange-them-in-a-circle-in-such-a-way-that-the-product-of-any-two-adjacent-numbers

Question Number 116356 by bemath last updated on 03/Oct/20 $$\mathrm{Let}\:\mathrm{S}\:=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…,\mathrm{48},\mathrm{49}\right\}\:.\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{it}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{select}\:\mathrm{n}\:\mathrm{numbers}\: \\ $$$$\mathrm{from}\:\mathrm{S}\:\mathrm{and}\:\mathrm{arrange}\:\mathrm{them}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\: \\ $$$$\mathrm{in}\:\mathrm{such}\:\mathrm{a}\:\mathrm{way}\:\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of} \\ $$$$\mathrm{any}\:\mathrm{two}\:\mathrm{adjacent}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{circle}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}\:\mathrm{100}? \\ $$ Terms…