Question

Daca a=1+2+2^2+2^3+...+2^59 , atunci aratati ca nr a + 1 este si patrat perfect si cub perfect

Answer 1

a=1+2+2²+2³+...+2⁵⁹/·2
2a=2+2²+2³+2⁴+...+2⁶⁰
a=2⁶⁰-1;
⇒a+1=2⁶⁰;⇒2⁶⁰=[2³⁰]²⇒patrat perfect;⇒[2²⁰]³⇒cub perfect;