Question

sa se scrie numarul 2009 ca o suma de puteri ale numarului 2

Answer 1

Salut,

2009:2 = 1004·2 + 1 = 502·2·2 + 1 = 251·2·2·2 + 1 = 251·2³ + 1 =
= (250 + 1)·2³ + 1= (125·2+1)·2³ + 1 = 125·2⁴ + 2³ + 1 = (124+1)·2⁴ + 2³ + 1 =
= 124·2⁴ + 2⁴ + 2³ + 1 = 62·2⁵ + 2⁴ + 2³ + 1 = 31·2⁶ + 2⁴ + 2³ + 1 = (30+1)·2⁶ + 2⁴ + 2³ + 1 = 30·2⁶ + 2⁶ + 2⁴ + 2³ + 1 = 15·2⁷ + 2⁶ + 2⁴ + 2³ + 1 =
= (14 + 1)·2⁷ + 2⁶ + 2⁴ + 2³ + 1 = 14·2⁷ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 =
= 7·2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 = (2·3+1)·2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 =
= 3·2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 = (2+1)·2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 = 2¹⁰ + 2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 1 = 2¹⁰ + 2⁹ + 2⁸ + 2⁷ + 2⁶ + 2⁴ + 2³ + 2⁰.

Green eyes.