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Question Number 72824 by Rio Michael last updated on 03/Nov/19

$$fndallintegersnforwhich$$$$13\mid 4(n^2+1)$$

Answered by mind is power last updated on 03/Nov/19

$$\Rightarrow {\mathrm{n}}^2+1\equiv 0\left(13\right)$$$$\Rightarrow {\mathrm{n}}^2+1-26\equiv -26\left(13\right)$$$$\iff {\mathrm{n}}^2-25\equiv 0\left(13\right)$$$$\iff (\mathrm{n}-5)(\mathrm{n}+5)\equiv 0\left(13\right)$$$$\mathrm{sine}13\mathrm{is}\mathrm{prime}$$$$\Rightarrow 13\mid \mathrm{n}-5\vee 13\mid \mathrm{n}+5$$$$\Rightarrow \mathrm{n}=13\mathrm{k}+5\vee \mathrm{n}=13\mathrm{k}-5$$

Commented by Rio Michael last updated on 03/Nov/19

$$thankssomuchsir$$

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