Question Number 112573 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by Rasheed.Sindhi last updated on 08/Sep/20 $${Let}\:{two}\:{numbers}\:{are}\:\mathrm{10}{a}+{b}\:\& \\ $$$$\mathrm{10}{c}+{d}\:{with}\:\mathrm{10}{a}+{b}>\mathrm{10}{c}+{d} \\ $$$${After}\:{written}\:{beside}: \\ $$$$\mathrm{100}\left(\mathrm{10}{a}+{b}\right)+\left(\mathrm{10}{c}+{d}\right)…
Question Number 112572 by Aina Samuel Temidayo last updated on 08/Sep/20 Commented by mr W last updated on 08/Sep/20 $${see}\:{Q}\mathrm{112533} \\ $$ Answered by mr…
Question Number 112535 by Aina Samuel Temidayo last updated on 08/Sep/20 $$\mathrm{Let}\:\mathrm{K}\:\mathrm{be}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\mathrm{factors} \\ $$$$\left(\mathrm{b}−\mathrm{a}\right)\:\left(\mathrm{not}\:\mathrm{necessarily}\:\mathrm{distinct}\right) \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\mathrm{integers}\:\mathrm{satisfying} \\ $$$$\mathrm{1}\leqslant\mathrm{a}\leqslant\mathrm{b}\leqslant\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest} \\ $$$$\mathrm{integer}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{2}^{\mathrm{n}} \:\mathrm{divides}\:\mathrm{K}. \\ $$$$ \\ $$…
Question Number 112465 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by floor(10²Eta[1]) last updated on 08/Sep/20 $$\mathrm{3}\mid\mathrm{3}.\mathrm{4}^{\mathrm{n}} +\mathrm{51}=\mathrm{3}\left(\mathrm{4}^{\mathrm{n}} +\mathrm{17}\right)\:\left(\mathrm{clearly}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}\right) \\ $$$$\mathrm{9}\mid\mathrm{3}.\mathrm{4}^{\mathrm{n}} +\mathrm{51}\Leftrightarrow\mathrm{3}\mid\mathrm{4}^{\mathrm{n}} +\mathrm{17}\Leftrightarrow\mathrm{3}\mid\left(\mathrm{4}^{\mathrm{n}}…
Question Number 112323 by Rasheed.Sindhi last updated on 07/Sep/20 $$\:_{\leqslant} ^{\geqslant} =\:\:\mathbb{SOLVE}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathcal{EQUATION}}_{} ^{\:_{\:\:\bullet} } \\ $$$$\:\:\:\boldsymbol{\mathrm{n}}−\lfloor\sqrt{\boldsymbol{\mathrm{n}}}\rfloor−\lfloor\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{n}}}\rfloor+\lfloor\sqrt[{\mathrm{6}}]{\boldsymbol{\mathrm{n}}}\rfloor=\mathrm{2016} \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated…
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Question Number 46760 by arcana last updated on 31/Oct/18 $${how}\:{many}\:{natural}\:{solutions}\:{exist} \\ $$$${to} \\ $$$${x}+{y}+{z}=\mathrm{11},\:{x},{y},{z}\in\mathbb{N} \\ $$ Commented by MrW3 last updated on 31/Oct/18 $${no}.\:{of}\:{ways}\:{to}\:{put}\:\mathrm{11}\:{objects}\:{into}\:\mathrm{3}\:{containers}: \\…
Question Number 46751 by Joel578 last updated on 31/Oct/18 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{4}\:\mathrm{distinct}\:\mathrm{positive}\:\mathrm{integers} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{each}\:\mathrm{integer}\:\mathrm{divides}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{remaining}\:\mathrm{integers}.\: \\ $$ Commented by MrW3 last updated on 31/Oct/18 $${n},\mathrm{2}{n},\mathrm{3}{n},\mathrm{6}{n}\:{with}\:{n}\in\mathbb{N} \\…
Question Number 46592 by Tawa1 last updated on 29/Oct/18 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{to}:\:\:\:\mathrm{7x}\:+\:\mathrm{5y}\:+\:\mathrm{15z}\:+\:\mathrm{12w}\:=\:\mathrm{149} \\ $$ Commented by Tawa1 last updated on 29/Oct/18 $$\mathrm{No}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{sir} \\ $$ Answered by MrW3…
Question Number 46576 by Tawa1 last updated on 28/Oct/18 $$\mathrm{Please}\:\mathrm{any}\:\mathrm{note}\:\mathrm{on}\:\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit},\:\mathrm{first}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{and}\:\mathrm{first}\:\mathrm{three}\:\mathrm{digits} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{power} \\ $$ Commented by hassentimol last updated on 30/Oct/18 $$ \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{sure}\:\mathrm{at}\:\mathrm{all}\:\mathrm{but}\:\mathrm{I}\:\mathrm{think}\:\mathrm{that},\:\mathrm{according} \\…