JJ278不会啊~~

橘子树的冬天

p,q是不同质数，m,n 是integer，问如果（mp+nq）/pq是整数，问以下哪个一定成立：
1 p是n的factor
2 mp是pq的factor

sdcar2010

（mp+nq）/pq = a

mp + nq = apq

p*(aq-m) = nq

Since p and q are both prime numbers, then p has to be a factor of n, because it cannot be a factor of q. (1) was right.

And q has to be a facotr of (aq-m) because it cannot be a factor of p.

So q*b=aq -m. m=q*(a-b). So q is a factor of m. Then (2) was not right.

mfdfz

原式化简可得：m/q+n/p 所以如果这个是整数，那么m/q和n/p都是整数
1.p是n的因数……我觉得对啊，不然n/p不会是整数，所以成立
2.mp是pq的因数即m是q的因数，这样的话m/q肯定不是整的，所以不成立

carbonzju

狗主人表示此题应该是做错的，条件2记不清了，请考试时仔细看题。

橘子树的冬天

（mp+nq）/pq = a

mp + nq = apq

p*(aq-m) = nq

Since p and q are both prime numbers, then p has to be a factor of n, because it cannot be a factor of q. (1) was right.

And q has to be a facotr of (aq-m) because it cannot be a factor of p.

So q*b=aq -m. m=q*(a-b). So q is a factor of m. Then (2) was not right.

-- by 会员 sdcar2010 (2011/4/9 13:24:46)

THX~  u r soooooooo brilliant!!

橘子树的冬天

狗主人表示此题应该是做错的，条件2记不清了，请考试时仔细看题。

-- by 会员 carbonzju (2011/4/9 13:53:11)

原来是狗主人~~  那个。。。JJ里貌似有这道题的变体   变成DS的。。。考试时还是看看清楚！！