Category: Number Theory

Question Number 124130 by soumyasaha last updated on 01/Dec/20 $$$$$$\mathrm{Let}\mathrm{P}={(3\sqrt{6}+7)}^{89}\mathrm{and}\mathrm{F}\mathrm{is}\mathrm{fractional}$$$$\mathrm{part}\mathrm{of}\mathrm{P}.$$$$\mathrm{Then}\mathrm{find}\mathrm{the}\mathrm{remainder}\mathrm{when}$$$$\left(\mathrm{PF}\right)+{\left(\mathrm{PF}\right)}^2+{\left(\mathrm{PF}\right)}^3\mathrm{is}\mathrm{divided}\mathrm{by}31.$$ Answered by…

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Question Number 188196 by cortano12 last updated on 26/Feb/23 $$\left(1\right)\mathrm{solve}\mathrm{Diopthantine}\mathrm{equation}$$$$754\mathrm{x}+221\mathrm{y}=13$$$$\left(2\right)\mathrm{find}\mathrm{the}\mathrm{number}\mathrm{abcd}$$$$\mathrm{such}\mathrm{that}4\times \left(\mathrm{abcd}\right)=\mathrm{dcba}$$ Commented by ARUNG_Brandon_MBU last updated on 26/Feb/23…

Question Number 121834 by bemath last updated on 12/Nov/20 Answered by liberty last updated on 12/Nov/20 $$\mathrm{we}\mathrm{have}\gcd (93,27)=3\mathrm{and}6\mathrm{divides}\mathrm{by}3$$$$\mathrm{therefore}\mathrm{there}\mathrm{exist}\mathrm{solutions}.$$$$\mathrm{we}\mathrm{have}93=3\times 27+12\wedge 27=2\times 12+3$$$$12=4\times 3+0$$$$\:\mathrm{3}\:=\:\mathrm{1}×\mathrm{27}−\mathrm{2}×\mathrm{12}\:…

Question Number 187296 by anurup last updated on 15/Feb/23 $$\mathrm{Prove}\mathrm{that}\mathrm{for}\mathrm{n}⩾4,{\mathrm{S}}_n=\underset{k=1}{\sum ^n}{k}^{k!}\mathrm{is}\mathrm{never}\mathrm{a}\mathrm{perfect}\mathrm{cube}.$$ Commented by anurup last updated on 15/Feb/23 $$\mathrm{Please}\:\mathrm{solve}\:\mathrm{this}. \…