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Category: Algebra

Given-A-n-2-2n-2-B-n-2-2n-2-n-N-1-Show-that-divisor-of-A-which-divise-n-can-also-divise-2-Show-that-all-common-divisor-of-A-and-B-can-divise-4n-

Question Number 118193 by mathocean1 last updated on 15/Oct/20 $${Given}\:{A}={n}^{\mathrm{2}} −\mathrm{2}{n}+\mathrm{2}\:,\:{B}={n}^{\mathrm{2}} +\mathrm{2}{n}+\mathrm{2} \\ $$$${n}\:\in\:\mathbb{N}^{\ast} −\left\{\mathrm{1}\right\}. \\ $$$${Show}\:{that}\:\forall\:{divisor}\:{of}\:{A}\:{which}\:{divise} \\ $$$${n}\:{can}\:{also}\:{divise}\:\mathrm{2}. \\ $$$${Show}\:{that}\:{all}\:{common}\:{divisor}\:{of}\: \\ $$$${A}\:{and}\:{B}\:{can}\:{divise}\:\mathrm{4}{n}. \\ $$…

factorise-x-4-4-

Question Number 118184 by mathocean1 last updated on 15/Oct/20 $${factorise}\:{x}^{\mathrm{4}} +\mathrm{4} \\ $$ Commented by bemath last updated on 16/Oct/20 $$\left({x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \:=\:\left({x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}}…

show-that-if-n-is-odd-n-n-2-3-is-even-

Question Number 118180 by mathocean1 last updated on 15/Oct/20 $${show}\:{that}\:{if}\:{n}\:{is}\:{odd}\:,\:{n}\left({n}^{\mathrm{2}} +\mathrm{3}\right)\:{is}\:{even}. \\ $$ Answered by floor(10²Eta[1]) last updated on 15/Oct/20 $$\mathrm{if}\:\mathrm{n}\:\mathrm{is}\:\mathrm{odd}\Rightarrow\mathrm{n}=\mathrm{2k}+\mathrm{1},\:\mathrm{k}\in\mathbb{Z} \\ $$$$\left(\mathrm{2k}+\mathrm{1}\right)\left(\left(\mathrm{2k}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}\right) \\…