Divisors

If x1,x2,x3,....,xk are the divisors of positive integer n. If Σxi=75 then find Σ(1/xi)?

[7]

10 Answers

1
Philip Calvert ·

hi can you tell
is xi is the set of all the divisors of n ?

33
Abhishek Priyam ·

its the lang given in the question.. :(

But i think it should be all divisors...
I solved it in 11th but when tried it now for revision i am clueless :(

33
Abhishek Priyam ·

Got it..

tx...

ignore this question...

[1]

1
gagar.iitk ·

can u share ur ans

1
Philip Calvert ·

ya it would help me

341
Hari Shankar ·

Let S = x1+x2+...+xn

Remember that if d is a divisor, then so is n/d.

2S = Σ1/xi+Σxi/n = S + 75/n

Hence S = 75/n

1
gagar.iitk ·

thanks

33
Abhishek Priyam ·

[1]

Yes i got same answer and sorry 4 not replying as there was a power cut..

1
Philip Calvert ·

how
2S = Σ1/xi+Σxi/n = S + 75/n [7]

sorry if its stupid but got a mental block presently [2]

33
Abhishek Priyam ·

x1.y1=n
x2.y2=n
..
.

so Σ1/xi=Σyi/n

yi are also the divisors hence the answer..

Hope its clear..

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