If a,b,c are the 3 positive integers 1/a +1/b +1/c > 6/abc (bc+ac+ab)/abc >6/abc so (bc+ac+ab)>6 The lowest positive integers that are different are 1,2,3 so the lowest value that (bc+ac+ab) could have is 1•2+2•3+1•3=2+6+3= 11 therefore 1/a +1/b +1/c > 6/abc is true
