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 $${any}\:{integer}\:{p}\:{can}\:{be}\:{expressed}\:{in}\:{the}\:{form} \\…
Question Number 109410 by bobhans last updated on 23/Aug/20 $${solve}\:\begin{cases}{{x}\equiv\mathrm{3}\:\left({mod}\:\mathrm{5}\right)}\\{{x}\equiv\:\mathrm{1}\:\left({mod}\:\mathrm{7}\right)}\\{{x}\:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{8}\right)}\end{cases} \\ $$ Commented by bobhans last updated on 24/Aug/20 $${thank}\:{you}\:{all}\:{master} \\ $$ Answered by 1xx…
Question Number 174566 by RajiYusuf last updated on 04/Aug/22 Answered by aleks041103 last updated on 05/Aug/22 $${f}\left({n}\right)=\mathrm{2}{n}−\sigma\left({n}\right) \\ $$$$\sigma\left({n}\right)=\underset{{i}>\mathrm{0},{i}\mid{n}} {\sum}{i} \\ $$$$\sigma\left({p}^{\mathrm{2}} \right)=\mathrm{1}+{p}+{p}^{\mathrm{2}} \\ $$$$\Rightarrow{f}\left({p}^{\mathrm{2}}…
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Question Number 108516 by Rasheed.Sindhi last updated on 17/Aug/20 $$\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 $${if}\:{x}>\mathrm{0}:…
Question Number 108264 by Rasheed.Sindhi last updated on 15/Aug/20 $${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 $$\mathrm{50}=\mathrm{2}×\mathrm{5}^{\mathrm{2}}…
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Question Number 42291 by Joel578 last updated on 22/Aug/18 $${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 $$\mathrm{19}{x}+\mathrm{49}{y}=\mathrm{1080} \\ $$$$\mathrm{19}\left({x}+{y}\right)+\mathrm{30}{y}=\mathrm{30}×\mathrm{36} \\…
Question Number 41754 by Tawa1 last updated on 12/Aug/18 Answered by candre last updated on 12/Aug/18 $$\mathrm{we}\:\mathrm{have}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{1000}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{have}\:\mathrm{3} \\ $$$$\mathrm{3}×× \\ $$$$×\mathrm{3}× \\ $$$$××\mathrm{3} \\ $$$$\mathrm{separating}\:\mathrm{cases}…
Question Number 172210 by Rasheed.Sindhi last updated on 24/Jun/22 $$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{in}}\:\mathbb{N}: \\ $$$$\mathrm{6}^{\boldsymbol{\mathrm{x}}} +\mathrm{6}^{\boldsymbol{\mathrm{y}}} =\mathrm{222} \\ $$ Commented by infinityaction last updated on 24/Jun/22 $$\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{3},\mathrm{1}\right) \\…