Question

Demonstrati ca :
a) 3 divide pe (3a+6b+9c)
b) 10 divide (9 la puterea n +9 la puterea n+1), n apartine N
c) 7 divide (1001+2002+...+9009)
d) 11  divide (2 la puterea 44 +2 la puterea 47+ 2 la puterea 45)
AJUTOR!!!!!

Answer 1

a) 3 divide pe (3a+6b+9c)

3a+6b+9c=3(a+2b+3c) deci divide 3 acest numar

b) 10 divide (9 l^n +9 ^ n+1), n apartine N


9 ^ n +9 ^ n+1=9 ^n(1+9)=9^ n*10 deci divide 10 acest numar


c) 7 divide (1001+2002+...+9009)

1001+2002+...+9009=1001(1+2+...+9)=1001*9*10:2=1001*45=45045=7*6435 deci divide 7 acest numar

d) 11 divide (2 ^44 +2^47+ 2^45)

2 ^ 44 +2 ^47+ ^ 45=2^44(1+2^3+2)=2^44*11 deci div 11 acest numar