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Category: Number Theory

Question-109729

Question Number 109729 by lazygorilla last updated on 25/Aug/20 Answered by prakash jain last updated on 25/Aug/20 $$\mathrm{1}+{x}+{x}^{\mathrm{2}} +..+{x}^{{n}−\mathrm{1}} =\frac{\left({x}^{{n}} −\mathrm{1}\right)}{{x}−\mathrm{1}}\:\:\:\left({x}\neq\mathrm{1}\right) \\ $$$$\:\:\:\:\left(\mathrm{Geometric}\:\mathrm{Progression}\right) \\ $$$$\mathrm{2}^{\mathrm{0}}…

Prove-that-any-integer-can-be-expressed-as-in-the-form-of-4k-or4k-1-or-4k-2-

Question Number 44059 by paro123 last updated on 20/Sep/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{any}\:\mathrm{integer}\:\mathrm{can}\:\mathrm{be}\:\mathrm{expressed}\: \\ $$$$\mathrm{as}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{4k}\:\mathrm{or4k}\underset{−} {+}\mathrm{1}\:\mathrm{or}\:\mathrm{4k}\underset{−} {+}\mathrm{2}. \\ $$ Answered by kunal1234523 last updated on 21/Sep/18 $${any}\:{integer}\:{p}\:{can}\:{be}\:{expressed}\:{in}\:{the}\:{form} \\…

Question-174566

Question Number 174566 by RajiYusuf last updated on 04/Aug/22 Answered by aleks041103 last updated on 05/Aug/22 $${f}\left({n}\right)=\mathrm{2}{n}−\sigma\left({n}\right) \\ $$$$\sigma\left({n}\right)=\underset{{i}>\mathrm{0},{i}\mid{n}} {\sum}{i} \\ $$$$\sigma\left({p}^{\mathrm{2}} \right)=\mathrm{1}+{p}+{p}^{\mathrm{2}} \\ $$$$\Rightarrow{f}\left({p}^{\mathrm{2}}…

If-x-1-x-2-x-0-prove-that-x-n-1-x-n-2-n-Z-

Question Number 108516 by Rasheed.Sindhi last updated on 17/Aug/20 $$\mathrm{If}\:\mathrm{x}+\frac{\mathrm{1}}{\mathrm{x}}=\mathrm{2}\left(\mathrm{x}\neq\mathrm{0}\right),\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\mathrm{x}^{\mathrm{n}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{n}} }=\mathrm{2}\:\:\forall\:{n}\in\:\mathbb{Z} \\ $$ Commented by mr W last updated on 17/Aug/20 $${if}\:{x}>\mathrm{0}:…

Find-out-x-such-that-lcm-50-80-x-2800-lcm-56-84-x-840-

Question Number 108264 by Rasheed.Sindhi last updated on 15/Aug/20 $${Find}\:{out}\:{x},\:{such}\:{that}: \\ $$$$\mathrm{lcm}\left(\mathrm{50},\mathrm{80},{x}\right)=\mathrm{2800}\:\wedge\:\mathrm{lcm}\left(\mathrm{56},\mathrm{84},{x}\right)=\mathrm{840} \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mr W last updated on 15/Aug/20 $$\mathrm{50}=\mathrm{2}×\mathrm{5}^{\mathrm{2}}…

y-1080-19x-49-x-y-Z-Find-x-y-

Question Number 42291 by Joel578 last updated on 22/Aug/18 $${y}\:=\:\frac{\mathrm{1080}\:−\:\mathrm{19}{x}}{\mathrm{49}}\:\:\:\:\:\:\:\:\left({x},{y}\:\in\:\mathbb{Z}\right) \\ $$$$\mathrm{Find}\:\left({x},{y}\right) \\ $$ Answered by ajfour last updated on 22/Aug/18 $$\mathrm{19}{x}+\mathrm{49}{y}=\mathrm{1080} \\ $$$$\mathrm{19}\left({x}+{y}\right)+\mathrm{30}{y}=\mathrm{30}×\mathrm{36} \\…