Hey everyone,
I am working on this integer decomposition problem that I cant figure out. I would really apperciate your help on this.
Here is the problem:
It is known that every integer n greater than 17 may be written as the sum of three distinct integers, each greater than one, that are pairwise relatively prime; that is, no pair of the three integers have a common prime factor. Stated another way, their greatest common divisor is 1. To illustrate this fact, write a program that reads values of n from successive input lines and for each n show a decomposition of n into the sum of three integers a, b, and c by outputting a line of the form:
n = a + b + c
Your program may output any pairwise relatively prime decomposition. Furthermore the order of a, b, and c does not matter. Read n from command line.
This is what I have so far:
int gcd( int i, int j ) ;
int decompose( int x ) ;
int i, j, k ;
#include <stdio.h>
#include <stdlib.h>
int main( int argc, char *argv[] ) {
int n, a, b, c ;
n = atoi( argv[1] ) ;
decompose( n ) ;
printf( "\nInteger decomposition of %d is %d + %d + %d\n\n", n, a, b, c ) ;
return 0 ;
}
int gcd( int i, int j ) {
int x, y ;
if( i > j ) {
x = i ;
y = j ;
}
else {
y = i ;
x = j ;
}
if( x % y == 0 ) return y ;
else
return gcd( y, ( x % y ) ) ;
}
int decompose( int x ) {
int i, j, k ;
for( i = 1 ; i < x ; i++ ) {
for( j = ( i + 1 ) ; j < x ; j++ ) {
for( k = ( j + 1 ) ; k < x ; k++ ) {
if( ( i + j + k ) == x ) printf( "%d %d %d", i, j, k ) ;
if( ( gcd (i, j ) == 1 ) && ( gcd( j, k ) == 1 ) && ( gcd ( k, i ) == 1 ) ) ;
}
}
}
return 0 ;
}I would really appreciate if someone could show me what is wrong with this code. Thanks in advance.
