Less is More

Number Theory Level 2

108 x + 63 y = 9 108x + 63y = 9

Both x and y are integers.

Find the smallest possible positive value of x.


The answer is 3.

Ryan Teo by Ryan Teo , 23, Singapore

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

Aakash Singh
Apr 12, 2014

please paraphrase your question.Mention that x is a natural number and y is an integer.You can even take x=-4 which is smaller than 3.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

108x+63y=9 =>12x+7y=1 => x=3,y=-5 => 36-35=1

Aakash Singh - 7 years, 2 months ago

Problem statement is not correct...(-4,7) satisfies the relation. From here on, (x-7,y+12) always satisfies the solution and smallest possible value of x can go to -inf. So please change the statement which says (x) is a +ve integer (and not y).

Vishrant Goyal - 7 years, 1 month ago

3 is the smallest positive integer x can have (where y=-5)so that 108 3+63 -5=9

Mohammed Ashiq - 7 years, 1 month ago

it's simple. X=3

Abrar Rafid - 7 years, 1 month ago

Its simple
divide a by 9. u get 12x+7y=9 take 12x + 7y using trial method by putting x =1,2,3 u can find the answer easily

Avudaiappan Siva - 7 years, 1 month ago
Adil Shaikh
Apr 17, 2014

108x+63y=9 take 9 as common so 12x+7y=1, now put x=1,2,3,4....., when u put x=3 so y will be y=-5, right ans is 3.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

x=-17 12(-18)+7(31)=1

Divya Sushritha - 7 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...