Question

Aflati nr n ptr care 2^n×5^n-1=2000 Calculati restul împărțirii nr 2+2^n+2^n+1 La 3 pentru orice nr natural n

Answer 1

2^n•5^(n-1)=2000

2^n•5^n /5=2000

10^n=5•2000

10^n=10000=10^4

deci, n=4

a=2+2^n+2^(n+1)

a=2+2^n(1+2)

a=3•2^n  +2

a:3=(3•2^n  +2):3 =2^n rest 2