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Yanuska11
@Yanuska11
November 2021
1
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ДЕЛИТСЯ ЛИ НА 2009
СРОЧНО
(2010^2010)-1
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IrkaShevko
Verified answer
2010²⁰¹⁰ - 1 = (2010 - 1)(2010²⁰⁰⁹ + 2010²⁰⁰⁸ + ... + 2010 + 1) =
= 2009(2010²⁰⁰⁹ + 2010²⁰⁰⁸ + ... + 2010 + 1)
=> да, делится
использовали формулу:
aⁿ - bⁿ = (a - b)(aⁿ⁻¹ + aⁿ⁻²b + aⁿ⁻³b² + ... + abⁿ⁻² + bⁿ⁻¹)
4 votes
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Answers & Comments
Verified answer
2010²⁰¹⁰ - 1 = (2010 - 1)(2010²⁰⁰⁹ + 2010²⁰⁰⁸ + ... + 2010 + 1) == 2009(2010²⁰⁰⁹ + 2010²⁰⁰⁸ + ... + 2010 + 1)
=> да, делится
использовали формулу:
aⁿ - bⁿ = (a - b)(aⁿ⁻¹ + aⁿ⁻²b + aⁿ⁻³b² + ... + abⁿ⁻² + bⁿ⁻¹)