標題:
求方程123x+57y=531的整數解
發問:
求方程123x+57y=531的整數解 請解釋得盡量淺易易明 thx~ 更新: Let y = v + 4.................(1) Let x = u + 2........(2) 呢到點黎 更新 2: Let y = v + 4.................(1) Let x = u + 2........(2) 點黎
最佳解答:
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To find the integral solution for 123x + 57y = 531, first we reduce the equation to: Before finding the general solution, we need to find one simple solution first. by guess, we have 41(-1) + 19(2) = 3 and hence, 41(-59) + 19(118) = 177 so one such solution is (-59, 118) 41x + 19y = 177 Since LCM (41, 19) = 779, so 41(-59) + 779k - 779k + 19(118) = 177, where k is an integer 41(-59 + 19k) + 19(118 - 41k) = 177 So the general integral solution is x = -59 + 19k, y = 118 - 41k, where k is an integer For example, take k = 0, we get the solution we guessed before.
其他解答:
When x = 0 , y = 531/57 = 9.3. So for both x and y to be positive integers, y must be between 0 and 9. Let y = v + 4.................(1) When y = 0, x = 531/123 = 4.3, So x is between 0 and 4. Let x = u + 2........(2) Sub. (1) and (2) into the equation, we get 123(u + 2) + 57(v + 4) = 531 123u + 246 + 57v + 228 = 531 123u + 57v = 57 so u = 0 and v = 1. Therefore, x = 0+ 2 = 2 and y = 1 +4 = 5.|||||123x+57y=531 一起除3 41x+19y=177 因為x,y是整數 when x=1 177- 41 x1 = 136 不整除於19 when x=2 177-82 = 95 整除於19 所以x=2正確,將x=2代入 41x+19y=177 y=5 when x=3 177-3x41=177-123=54不整除於19 when x=4 177-4x41=13 不整除於１９ 答案y=5 x=2 123(2) + 57(5)=531 246+285=531 正解！
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