n=2p.3q
how many factors of n2 are smaller than n
(edit) but do not divide n?
9let x be no of factors of n2 less than n
now 2x +1 =tot no of factors of n2 ( by symmetry no of factors>n = that<n)
ie 2X+1=(2p+1)(2q+1)
hence X=((2p+1)(2q+1)-1)/2
of this (q+1)(p+1) -1 are factors of n itself
so req ans is (3pq + p + q +1)/2 after subtraction and simplification
62OOps varun u caught me.. this should have been any factor of n2 which does not divide n :)
sorry dude :)
(edited the question accordingly!!)
But i guess we should try this one now :P
B.t.w ur answer for this part is correct :)
1Any number smaller than n is not divisible by n right ?
So any factor of n2 lass than n is not divisible by n right ?
62Did u read the question!
" are smaller than n but not divisible by n?"
1n = 25.30
n2 = 210
The number of factors of 1024 is 11.
Therefore the number of factors of n2 less than n is (11-1)/2 = 5.
5 + 0 + 2( 5 * 0) = 5
1Lol I got that result by just seeing the different values for number of factors for n2 for different values of p and q.
So I can't be 100% sure.. but w/e value of p and q I substitute, I am getting the answer..
And the result is only for p≥0 and q≥0.
62HINT
Find the number of factors of n2 < n
Find the number of factors of n which are smaller than n!
Are all factors of n also factors of n2?
If u answer these three simple questions individually u will reach the answer :)
62(2p+1)(2q+1) - (q+1)(p+1) ??
No dear.. this is an obvious choice.. but unfortunately not the correct solution!
Ur giving this answer is obvious! but no! In an objective paper i am damn sure 1/2 th eppl wud have givne this as the answer :)
1smaller than n but not divisible by n
Any factor of n2smaller than n is not divisible by n right ?
