Prime Style

Number Theory Level 4

Let p p and q q be distinct primes.Then the number of positive integer solutions (x and y are distinct) of the equation 1 x \frac{1}{x} + 1 y \frac{1}{y} = 1 p ∗ q \frac{1}{p*q} is ? ?


The answer is 9.

Rajdeep Brahma by rajdeep brahma , 21, India

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

Rajdeep Brahma
May 28, 2018

x= p ∗ q ∗ y y − p ∗ q \frac{p*q*y}{y-p*q} = p 2 ∗ q 2 y − p ∗ q \frac{p^2*q^2}{y-p*q} + p ∗ q p*q ...So (y-p q) divides p 2 ∗ q 2 p^2*q^2 ....now p & q are both primes so p 2 ∗ q 2 p^2*q^2 stuff has (2+1) (2+1)=9 factors and yess we are done :)....hope u liked the problem...it appeared in NEST 2015....

5 Helpful 1 Interesting 0 Brilliant 0 Confused

Nice problem! Thank you!!! (+1)

Noel Lo - 3 years ago

Log in to reply

Thanks !!😊😊

rajdeep brahma - 3 years ago

The answer should be 8. From total of 9 cases, there exists a case wherein x=y=2pq. Since the problem explicity states that x & y are distinct, there must be 9-1 = 8 solutions

Aeram Albo - 2 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...