Category: Number Theory

Question Number 100583 by Rio Michael last updated on 27/Jun/20 $$\mathrm{A}\mathrm{transformation}f\mathrm{on}\mathrm{a}\mathrm{complex}\mathrm{plane}$$$$\mathrm{is}\mathrm{defined}\mathrm{by}{z}^{\prime }=(1+i)z-3+4i$$$$\mathrm{show}\mathrm{that}f\mathrm{is}\mathrm{a}\mathrm{simultitude}\mathrm{with}\mathrm{radius}r\mathrm{and}\mathrm{centre}$$$$\mathrm{\Omega }\mathrm{to}\mathrm{be}\mathrm{determined}.$$$$\mathrm{Determine}\mathrm{to}\mathrm{the}\mathrm{invariant}\mathrm{point}\mathrm{under}f.$$ Terms of Service Privacy…

Question Number 35005 by Rasheed.Sindhi last updated on 14/May/18 $$\mathrm{Find}\mathrm{remainder}\mathrm{when}$$$$1!+2!+3!+\dots +99!+100!$$$$\mathrm{is}\mathrm{divided}\mathrm{by}12.$$ Answered by rahul 19 last updated on 14/May/18 $$\mathrm{9}\:.…

Question Number 100178 by bobhans last updated on 25/Jun/20 $$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{ordered}\mathrm{pairs}\mathrm{of}\mathrm{positif}$$$$\mathrm{integers}(\mathrm{x},\mathrm{y})\mathrm{that}\mathrm{satisfy}{\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{xy}=37$$ Answered by 1549442205 last updated on 25/Jun/20 $$\mathrm{x}^{\mathrm{2}} −\mathrm{xy}+\mathrm{y}^{\mathrm{2}}…

Question Number 34385 by Rasheed.Sindhi last updated on 05/May/18 $$\mathrm{p},\mathrm{q}\in \mathbb{P}$$$$\mathrm{m},\mathrm{n}\in \{0,1,2,\dots \}$$$$\mathrm{How}\mathrm{many}\mathrm{pairs}\mathrm{are}\mathrm{there},\mathrm{whose}$$$$\mathrm{LCM}\mathrm{is}{\mathrm{p}}^{\mathrm{m}}{\mathrm{q}}^{\mathrm{n}},\mathrm{when}:$$$$\left(\mathrm{i}\right)(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{same}.$$$$\left(\mathrm{ii}\right)(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{different}.$$$$\:\:\:\:\left(\mathrm{Generalization}\:\mathrm{of}\:\mathrm{Q}#\:\mathrm{34358}\right) \…

Question Number 34358 by Rasheed.Sindhi last updated on 05/May/18 $$\mathrm{Determine}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{pairs}\mathrm{whose}$$$$\mathrm{LCM}\mathrm{is}144\mathrm{in}\mathrm{case},$$$$\left(\mathrm{i}\right)\mathrm{when}(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{same}.$$$$\left(\mathrm{ii}\right)\mathrm{when}(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{different}.$$ Commented by candre last updated on 05/May/18…