Question Number 178282 by Sheshdevsahu last updated on 14/Oct/22 $$ \\ $$$${find}\:{unit}\:{digit}\:{of}\: \\ $$$$\mathrm{1}^{\mathrm{1}} +\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +…….+\mathrm{63}^{\mathrm{63}} +\mathrm{64}^{\mathrm{64}} \\ $$ Answered by mr W last…
Question Number 112575 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by Rasheed.Sindhi last updated on 09/Sep/20 $${x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} =\mathrm{1376} \\ $$$$\because\mathrm{4}\mid\mathrm{1376}\:\:\:\:\:\therefore\:\mathrm{4}\mid{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} \\…
Question Number 112573 by Aina Samuel Temidayo last updated on 08/Sep/20 Answered by Rasheed.Sindhi last updated on 08/Sep/20 $${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…
Question Number 112308 by bemath last updated on 07/Sep/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
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} \\…