Question

qual o resto da divisão de 2^2015 por 5?

Answer 1

2^2015\5

2^2015=3,76219466227E606

3,76219466227E606\5=7,52438932454E605

Answer 2

Resposta:

Usando o pequeno teorema de Fermat

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p:primo

a:inteiro

a^p =a (mod p)   (i)

a^(p-1)=1 (mod p)   (ii)

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2^(2015) por 5  .. queremos o resto

N=2^(2015) (mod 5)

2015 |  4  

3       503

resto =2^(4*503 +3)  (mod 5)

resto= (2^503)^4  *  2^3 (mod 5)  

**usando (ii)  resto = (2^503)^4 (mod 5) =1

resto  = 1 * 2³  (mod 5)  

resto o =2³ (mod 5) = 3