The integers 1 2 3 have the property that each divides the s

The integers 1, 2, 3 have the property that each divides the sum of other two. Indeed, for each positive integer a, the integer a, 2a, 3a have the property that each divides the sum of other two. show that the following statement is false:

answer guide:

disprove there exists positive integer b < c < d (where c does not equal 2b and b does not equal 3b) such that b | b+d and d | b+c

proving: for every tripled positive integers b < c < d such that b | c+d , c | b+d , d | b+c, then c = 2b and d = 3b

Solution