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Question Number 202698 by Bambamamoudou last updated on 31/Dec/23

$$determinelerestedeladivisioneucludiennede{2023}^{2019}par13$$

Answered by Rasheed.Sindhi last updated on 01/Jan/24

$$\because gcd(2023,13)=1$$$$\therefore {2023}^{\varphi \left(13\right)}\equiv 1\left(mod13\right)$$$${2023}^{12}\equiv 1\left(mod13\right)$$$${\left({2023}^{12}\right)}^{168}{\left(2023\right)}^3\equiv {2023}^3\left(mod13\right)$$$${2023}^{2019}\equiv {(13\times 155+8)}^3\left(mod13\right)$$$${2023}^{2019}\equiv {\left(8\right)}^3=512\equiv 5\left(mod13\right)$$

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