Question Number 47310 by Meritguide1234 last updated on 08/Nov/18 Commented by MJS last updated on 08/Nov/18 $${x}\neq{y}\neq{z}\neq\mathrm{0}\:\mathrm{I}\:\mathrm{guess}. \\ $$$$\mathrm{but}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that}\:\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{triple}\:{xyz}\:\mathrm{for}\:{n}>\mathrm{2} \\ $$$$\mathrm{so}\:\mathrm{we}\:\mathrm{only}\:\mathrm{have}\:\mathrm{to}\:\mathrm{show}\:\mathrm{for}\:{n}=\mathrm{2}\:\mathrm{and}\:\mathrm{in}\:\mathrm{this} \\ $$$$\mathrm{case}\:\mathrm{it}'\mathrm{s}\:\mathrm{obviously}\:\mathrm{true}\: \\ $$…
Question Number 178277 by Sheshdevsahu last updated on 14/Oct/22 $$ \\ $$$${if}\:\mathrm{2}^{{pq}} −\mathrm{2}^{{rs}} =\mathrm{32};\:{where}\:{p},{q},{r},{s}\in\mathbb{Z}\: \\ $$$${then}\:{possible}\:{values}\:{of} \\ $$$${p}\:+\:{q}\:+\:{r}\:+\:{s}\:=\:?? \\ $$$$ \\ $$ Terms of Service…
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…
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