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)
