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Category: Number Theory

Find-the-last-digit-from-2-400-2-320-2-200-2-160-2-200-2-160-

Question Number 191862 by cortano12 last updated on 02/May/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{from}\: \\ $$$$\:\left(\mathrm{2}^{\mathrm{400}} −\mathrm{2}^{\mathrm{320}} \right)\left(\mathrm{2}^{\mathrm{200}} +\mathrm{2}^{\mathrm{160}} \right)\left(\mathrm{2}^{\mathrm{200}} −\mathrm{2}^{\mathrm{160}} \right) \\ $$ Commented by BaliramKumar last updated…

What-is-the-remainder-f-149-when-divided-by-139-

Question Number 191710 by pete last updated on 29/Apr/23 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{f}\:\mathrm{149}!\:\mathrm{when}\:\mathrm{divided} \\ $$$$\mathrm{by}\:\mathrm{139}? \\ $$ Commented by Rasheed.Sindhi last updated on 29/Apr/23 $$\mathrm{149}!=\mathrm{1}.\mathrm{2}.\mathrm{3}…\mathrm{138}.\mathrm{139}.\mathrm{140}…\mathrm{148}.\mathrm{149} \\ $$$$\therefore\:\mathrm{149}!\mathrm{mod139}=\mathrm{0} \\…

Question-125959

Question Number 125959 by bramlexs22 last updated on 15/Dec/20 Answered by liberty last updated on 15/Dec/20 $${Let}\:{q}\:{denote}\:{the}\:{numbers}\:{of}\:{eggs}\:{originally} \\ $$$${in}\:{the}\:{basket}.\:{We}\:{want}\:{to}\:{find}\:{the}\:{least}\:{number} \\ $$$${of}\:{eggs}\:{in}\:{the}\:{basket}.\: \\ $$$$\Leftrightarrow\:{q}\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{2}\right)\:\equiv\:\mathrm{1}\left({mod}\:\mathrm{3}\right)\equiv\:\mathrm{1}\left({mod}\:\mathrm{5}\right)\:\equiv\:\mathrm{0}\:\left({mod}\:\mathrm{7}\right) \\ $$$${the}\:{first}\:{three}\:{congruences}\:{then}…

The-number-of-4-digit-numbers-that-contain-the-number-6-and-are-divisible-by-3-is-

Question Number 190569 by cortano12 last updated on 06/Apr/23 $$\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{4}−\mathrm{digit}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{contain}\:\mathrm{the} \\ $$$$\:\mathrm{number}\:\mathrm{6}\:\mathrm{and}\:\mathrm{are}\:\mathrm{divisible}\: \\ $$$$\:\mathrm{by}\:\mathrm{3}\:\mathrm{is}\:\_\_\_ \\ $$ Answered by talminator2856792 last updated on 06/Apr/23…