SITTERS:-

1) define N=2ⁿ(2ⁿ⁺¹ - 1) , nEN... such dat (2ⁿ⁺¹-1) is a prime no.

prove that:-

i) the sum of the divisors of N are 2N.

ii) the sum of the reciprocals of the divisors of N are 2.

2) find all continuous functions f : (0, infi) --> (0, infi) such that

f(1)=1 and

\frac{1}{2}\int_{0}^{x}{(f(t))^2dt} = \frac{1}{x}\left(\int_{0}^{x}{f(t)dt} \right)^2