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Question Number 131507 by Chhing last updated on 05/Feb/21

$$$$$$1/\mathrm{Show}\mathrm{that}{\left(2019\right)}^{2021}+{\left(2021\right)}^{2019}\mathrm{divided}\mathrm{by}2020$$$$2/\mathrm{Show}\mathrm{that}{2222}^{5555}+{5555}^{2222}\mathrm{divided}\mathrm{by}7$$$$$$

Answered by JDamian last updated on 05/Feb/21

$$1/$$$$({2019}^{2021}+{2021}^{2019})mod2020=$$$$=[{(2020-1)}^{2021}+{(2020+1)}^{2019}]mod2020=$$$$=[{(-1)}^{2021}+1^{2019}]mod2020=$$$$=(-1+1)mod2020=0$$$$$$

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