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Find-all-pairs-of-positive-integers-a-b-such-that-a-2-2ab-2-b-3-1-Z-

Question Number 166400 by naka3546 last updated on 20/Feb/22 $$\mathrm{Find}\:\:\mathrm{all}\:\:\mathrm{pairs}\:\:\mathrm{of}\:\:\mathrm{positive}\:\:\mathrm{integers}\:\left({a},{b}\right)\:\:\mathrm{such}\:\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} }{\mathrm{2}{ab}^{\mathrm{2}} \:−\:{b}^{\mathrm{3}} +\mathrm{1}}\:\:\in\:\:\mathbb{Z}^{+} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-166392

Question Number 166392 by leicianocosta last updated on 19/Feb/22 Answered by som(math1967) last updated on 19/Feb/22 $${n}=\mathrm{1} \\ $$$$\mathrm{3}^{\mathrm{4}} +\mathrm{2}^{\mathrm{7}} =\mathrm{81}+\mathrm{128}=\mathrm{209}=\mathrm{11}×\mathrm{19} \\ $$$${multiple}\:{of}\:\mathrm{11} \\ $$$$\:\mathrm{3}^{\mathrm{2}{m}+\mathrm{2}}…

k-1-n-ln-k-k-

Question Number 100843 by bachamohamed last updated on 28/Jun/20 $$\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\boldsymbol{{ln}}\left(\boldsymbol{{k}}\right)}{\boldsymbol{{k}}!}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-166358

Question Number 166358 by leicianocosta last updated on 19/Feb/22 Answered by naka3546 last updated on 19/Feb/22 $$\frac{\mathrm{3a}^{\mathrm{2}} +\mathrm{5}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:−\:\frac{\mathrm{3a}^{\mathrm{2}} +\mathrm{1}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:<\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{4}}{\mathrm{a}^{\mathrm{2}} −\mathrm{1}}\:<\:\mathrm{0} \\…

Question-166321

Question Number 166321 by mathls last updated on 18/Feb/22 Answered by alephzero last updated on 19/Feb/22 $${x}\:−\:{table} \\ $$$${y}\:−\:{cat} \\ $$$${z}\:−\:{turte} \\ $$$$\Rightarrow\:\begin{cases}{{y}+{x}−{z}\:=\:\mathrm{170}}\\{{z}+{x}−{y}\:=\:\mathrm{130}}\end{cases} \\ $$$${y}\:=\:\mathrm{170}−{x}+{z}…