Find-the-least-positive-integer-n-for-which-2-n-5-n-n-is-a-multiple-of-1000-

Question Number 160064 by HongKing last updated on 24/Nov/21

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{for} \\ $$$$\mathrm{which}\:\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}} \:-\:\boldsymbol{\mathrm{n}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{1000} \\ $$

Commented by Rasheed.Sindhi last updated on 24/Nov/21

$$\mathrm{For}\:\mathrm{n}=\mathrm{1000},\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}} \:-\:\boldsymbol{\mathrm{n}}\:-\mathrm{1}\:\mathrm{is}\:\mathrm{multiple} \\ $$$$\mathrm{of}\:\mathrm{1000}. \\ $$

Commented by HongKing last updated on 25/Nov/21

$$\mathrm{Yes}\:\mathrm{my}\:\mathrm{dear}\:\mathrm{Ser},\:\mathrm{I}\:\mathrm{think}\:\mathrm{so} \\ $$

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