离散数学What are the solutions of the linear congruence 3x = 4 (

离散数学
What are the solutions of the linear congruence 3x = 4 (mod 7)?
Solution: By Example 3 we know that -2 is an inverse of 3 modulo 7. Multiplying both sides
of the congruence by - 2 shows that
-2*3x = -2*4 (mod 7).
Because -6 = 1 (mod 7) and -8 = 6 (mod 7), it follows that if x is a solution, then x = -8 =6 (mod 7).
We need to determine whether every x with x = 6 (mod 7) is a solution. Assume that
x = 6 (mod 7). Then, by Theorem 5 of Section 3.4, it follows that
3x = 3 *6 = 18 = 4 (mod 7),
这句
Because -6 = 1 (mod 7) and -8 = 6 (mod 7), it follows that if x is a solution, then x = -8 =
6 (mod 7).


是根据什么得出的结论
 雾之松 1年前他留下的回答 已收到1个回答

pepper_2004 网友

该名网友总共回答了11个问题，此问答他的回答如下：采纳率：72.7%

它是用二元运算的性质求解的,3在模7下乘法下的逆元是-2,然后-8＝6(mod 7),得x=6.
－－－－
我是这样做的：正整数集{1,2,3,4,5,6}关于模7乘法构成群,1是单位元,3的逆元是5.
所以由3x=4(mod 7),左乘5,得x=20(mod 7),20=6(mod 7),所以x=6.
－－－－
也可以这样做,3x=4(mod 7),则3x-4被7整除,最小的正整数x即为6

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雾之松

二元运算的那个性质？

pepper_2004

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