Nice Math Olympiad Question | You should know this trick for this kind of questions

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This is the easiest by far. Just take 2^2021 as the common factor (not even factorisation because that requires you to be able to see the common factors by arranging the numbers around)
So from there you get 2^2021 (1 + 2^1 + 2^2- 2^3)
Therefore a = 7-8 = -1

RogueLawyer
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Again, I don't believe it's Olympiads question, too easy ⁉️🤔

omidkh
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Such simple examples. What level is this?

mitahaubica
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Where are you from ma'am. It I may ask

Devendr