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Question Number 41292 by behi83417@gmail.com last updated on 04/Aug/18

Answered by MJS last updated on 04/Aug/18

m=((n+1)/2)±((√(−3n^2 +6n+5))/2)  the root is only defined for n=0, 1, 2 and for  these values m∉N  ⇒ no solution

$${m}=\frac{{n}+\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{−\mathrm{3}{n}^{\mathrm{2}} +\mathrm{6}{n}+\mathrm{5}}}{\mathrm{2}} \\ $$$$\mathrm{the}\:\mathrm{root}\:\mathrm{is}\:\mathrm{only}\:\mathrm{defined}\:\mathrm{for}\:{n}=\mathrm{0},\:\mathrm{1},\:\mathrm{2}\:\mathrm{and}\:\mathrm{for} \\ $$$$\mathrm{these}\:\mathrm{values}\:{m}\notin\mathbb{N} \\ $$$$\Rightarrow\:\mathrm{no}\:\mathrm{solution} \\ $$

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