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Question Number 118180 by mathocean1 last updated on 15/Oct/20

$$showthatifnisodd,n(n^2+3)iseven.$$

Answered by floor(10²Eta[1]) last updated on 15/Oct/20

$$\mathrm{if}\mathrm{n}\mathrm{is}\mathrm{odd}\Rightarrow \mathrm{n}=2\mathrm{k}+1,\mathrm{k}\in \mathbb{Z}$$$$(2\mathrm{k}+1)({(2\mathrm{k}+1)}^2+3)$$$$=(2\mathrm{k}+1)({4\mathrm{k}}^2+4\mathrm{k}+4)$$$$=4(2\mathrm{k}+1)({\mathrm{k}}^2+\mathrm{k}+1)=\mathrm{even}\mathrm{because}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{multiple}\mathrm{of}2$$$$$$

Commented by mathocean1 last updated on 15/Oct/20

$$thanks$$

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