Question

aratati ca 12^n+1 +4^n+1 x 3^n+ 4^n+2x3^n este divizibil cu 32

Answer 1

12^n×12+(4×3)^n×4^1+(4×3)^n×4^2=
12^n(12+4+16)=
12^n×32 este divizibil cu 32
sau scriem
32|12^n×32
4^n+1=4^n×4^1
4^n+2=4^n×4^2
12^n=(4×3)^n=4^n×3^n