Going to the basics

Number Theory Level 2

Let b , c ≠ 0 b,c\ne 0 be two coprime integers and we define A = { b x + c y : b x + c y > 0 ; x , y are integers } A = \{ bx + cy : bx +cy>0 ; x,y \text{ are integers} \} . Find the infimum of the set A A .


The answer is 1.

Milind Blaze by Milind Blaze , 22, 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

Milind Blaze
Jun 5, 2016

If b and c are two non zero integers then for some integers x and y the gcd of the b,c is of the form bx+cy. More specificalky it is the least positive integer of the set containing numbers of fhe form bx+cy and hence would be the glb of the set of numbers of the form bx+cy where bx+cy is positive. Further if b,c are coprime, then gcd(b,c)=1. Hence inf(A)=1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...