Question

determinati msi n numere naturale astfel incat 2^m-2^n=120​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

$2^m -2^n = 120\\ \\ 2^m - 2^n = 64+32+16+8\\ \\ 2^m-2^n = 2^6+2^5+2^4+2^3\\ \\ 2^m - 2^n = 2^6+2^5+2^4+2^3+(2^2+2^1+1)-(2^2+2^1+1)\\ \\ 2^m-2^n = 2^7-1-(2^2+2^1+1)\\ \\ 2^m-2^n = 2^7 - 1-4-2-1\\ \\ 2^m-2^n = 2^7-2^3\\ \\ \Rightarrow m = 7,\quad n = 3$