1these are ISI questions .... give a try.... easy ones [bcoz mujhse ho gaya]
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
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1SITTERS are there in Travian ... tumne dhokha diya yeh naam rakh kar !