Problem 3

Number Theory Level 1

How many ordered pairs ( x ; y ) (x;y) of non-zero positive integers exists to: 2 x + 4 y = 63 2x+4y=63 ?


The answer is 0.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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.

2 solutions

Jitendra Kumar
Aug 1, 2014

Once you multiply any number to an even number, output always be even and after adding two even numbers you can not get an odd value. Hence output will be zero

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The g c d ( 2 ; 4 ) gcd(2;4) don't divide 63 63 , because g c d ( 2 ; 4 ) = 2 gcd(2;4)=2 and 63 63 is odd. Therefore do not have solution. Answer: 0 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...