Question

[thục hà]

chứng tỏ rằng :

a, 5²⁰⁰³ + 5²⁰⁰² + 5²⁰⁰¹ : 31

b, 4³⁹ + 4⁴⁰ + 4⁴¹ : 21 

giúp mik vs 

Answer 1

[Nguyễn Thanh Hiền]

a) Ta có :

\(5^{2003}+5^{2002}+5^{2001}\)

\(=5^{2001}\times5^2+5^{2001}\times5+5^{2001}\)

\(=5^{2001}\times\left(5^2+5+1\right)\)

\(=5^{2001}\times31\)

Vậy  \(5^{2003}+5^{2002}+5^{2001}⋮31\)

b) Ta có :

\(4^{39}+4^{40}+4^{41}\)

\(=4^{39}+4^{39}\times4+4^{39}\times4^2\)

\(=4^{39}\times\left(1+4+4^2\right)\)

\(=4^{39}\times21\)

Vậy  \(4^{39}+4^{40}+4^{41}⋮21\)

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