[英]Algorithms (textbook) by Dasgupta. Prob. 1.36 Square Roots
To begin I want to say that this is NOT a homework problem. 首先,我想说的不是作业问题。 I know stackoverflow condemns people who ask for homework solutions.
我知道stackoverflow谴责了寻求作业解决方案的人。 I merely doing this problem out of interest.
我只是出于兴趣解决这个问题。
This is the question that I am working on: 这是我正在研究的问题:
Need help with part (b), not (a) 需要(b)部分而不是(a)帮助
I believe I understand (a); 我相信我了解(a); I had my own answer but I managed to compare my solution with a Chegg preview solution (it doesn't show part (b)).
我有自己的答案,但我设法将自己的解决方案与Chegg预览解决方案进行了比较(未显示(b)部分)。 So far from my understanding of part (b) is the following:
到目前为止,我对(b)部分的理解仍是:
when they say 当他们说
x is a square root of a modulo p if a = x^2(mod p)
they mean: x = sqrt(a mod p) IF a = x^2(mod p).
他们的意思是:
x = sqrt(a mod p) IF a = x^2(mod p).
Now, where it says, 现在,它说,
if a has a square root modulo p, then a^((p+1)/4)
is such a square root 如果a的平方根为p,则
a^((p+1)/4)
就是这样的平方根
confuses me a lot. 让我很困惑 I'm not really sure what this line means!
我不太确定这行是什么意思!
if a has a square root modulo p, then a^((p+1)/4) is such a square root
= =
If there exists K such that K^2 mod p = a
, 如果存在K使得
K^2 mod p = a
,
then 然后
a^((p+1)/4) mod p = K
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