m and n

Two natural numbers m and n have natural divisors

a 1 , a 2 , . . . . . . . . . . . . . . . . , a p a_{1} , a_{2} , ................ , a_{p}

and

b 1 , b 2 , . . . . . . . . . . . . . . . . . . . . . . . . b q b_{1} , b_{2} , ........................ b_{q}

and it is known that

a 1 + a 2 + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + a p = b 1 + b 2 + . . . . . . . . . . . . . . . . . . . . . . . . . + b q a_{1} + a_{2} + .............................+ a_{p} = b_{1} + b_{2} + ......................... + b_{q}

1 a 1 + . . . . . . . . . . . . . . . . . . . . 1 a p = 1 b 1 + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . + 1 b q \frac{1}{a_{1}} + .................... \frac{1}{a_{p}} = \frac{1}{b_{1}} + ............................. + \frac{1}{b_{q}}

Find the value of m n \frac{m}{n}


The answer is 1.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Sunil Pradhan
Oct 21, 2014

As sum of divisors and sum of reciprocals of divisors is same, it is possible only if all divisors of m and n are same. i.e. both m and n are same so m/n = 1

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...