Question

det elementele multimii A={abc| 2^ab- 2^bc=2^ac}​

Answer 1

A={abc| 2^ab- 2^bc=2^ac}

2^ab- 2^bc=2^ac

2^ab- 2^bc =2^ac[2^(ab-ac)- 2^(bc-ac)]; am dat factor comun pe 2^ac

=>2^(ab-ac)- 2^(bc-ac)=1

2^(b-c)- 2^(bc-ac)=1

diferenta a doua nr pare nu poate fi 1 => 2^(bc-ac)=1 si 2^(b-c)=2

=> bc-ac=0  si b-c=1

bc=ac=> a=b si  c=b-1=a-1

=>abc∈{110; 221; 332; 443; 554; 665; 776; 887; 998}

A={110; 221; 332; 443; 554; 665; 776; 887; 998}

verificare:

2^11- 2^10=2^10 (A)

2^22- 2^21=2^21 (A)

…………………….

2^99- 2^98=2^98 (A)