How many solutions

Level pending

Given a a and b b are integers, how many distinct solutions for ( a , b ) (a,b) does the following equation have?

a b = a + b ab=a+b

1 3 0 2

Janardhanan Sivaramakrishnan by Janardhanan Sivaramakris… , 42

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

Solving for a we get a = b b − 1 a=\frac{b}{b-1} .

Now as a a is an integer, b − 1 b-1 divides b b .

The only consecutive numbers which satisfy this condition are for b = 0 , 2 b=0,2 giving ( a , b ) = ( 0 , 0 ) , ( 2 , 2 ) (a,b)=(0,0),(2,2)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...