Re: [中學] 聯立方程

[mack (腦海裡依然記得妳)]

※ 引述《KAINTS (RUKAWA)》之銘言：
: |150m-k|=50
: |240n-k|=20
: 其中m,n為整數，且k<1000
: m,n=???
: 有沒有什麼方法解比較快??
   k = 150m ±50
=> 20 = |240n-k| = |240n-150m±50|
=> ±2 = 24n-15m±5
=> 24n-15m = ±7 (無解)or ±3
=> 8n-5m = ±1
=> Case I:8n-5m=1
   => (m,n)=(3,2),(-5,-3),...,(-5-8a,-3-5a),...
   Case II:8n-5m=-1
   => (m,n)=(5,3),...,(5-8a,3-5a),...

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 1.170.217.25
推 KAINTS      :感謝