Well, I see this problem has already been solved, so I won't go into too much detail. As others have noted above, we can reduce to the case in which the lcm is 2a. We have a = b + c + d or 1 = b/a + c/a + d/a. Since lcm(a,b,c,d) is 2a, each of the three fractions in simplified form either has a numerator of 1 or 2 and at least one of the numerators is 2. It is sufficient to show that at least one of the denominators of the fractions is divisible by 3 or 5. It is easy to see that at least one denominator must be less than 6 since 1/6 + 2/7 + 2/7 < 2/7 + 2/7 + 2/7 < 1. If no denominator is 3 or 5, then one denominator must be either 2 or 4. Since the fraction is in lowest terms, the numerator must be 1, i.e. one of the fractions b/a, c/a, or d/a is either 1/2 or 1/4. By inspection, we see that this can't work (just play around with the fractions).
2016-03-26 22:41:00
·
answer #2
·
answered by ? 4
·
0⤊
0⤋
something about if popeye and the yetti transformed together they would make an invincible team. and would kill everything in it's path. and shoot fire.
lol. i don't know...
2006-09-04 20:17:26
·
answer #3
·
answered by Anonymous
·
0⤊
0⤋