Comments on: How many numbers are squares mod m http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/ The blog of John D. Cook Sat, 11 Feb 2012 22:42:11 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Algorithms: Links, News, Resources (1) « Angel “Java” Lopez on Blog http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-90340 Algorithms: Links, News, Resources (1) « Angel “Java” Lopez on Blog Tue, 28 Jun 2011 09:57:04 +0000 http://www.johndcook.com/blog/?p=925#comment-90340 [...] How many numbers are squares mod m http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/ [...] [...] How many numbers are squares mod m http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/ [...]

]]> By: Zoresvit http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-60642 Zoresvit Sat, 15 Jan 2011 07:53:33 +0000 http://www.johndcook.com/blog/?p=925#comment-60642 <i>isOdd(p) can be faster to determine than p != 2.</i> Ah, that's what I was interested about. Thank you! isOdd(p) can be faster to determine than p != 2.
Ah, that’s what I was interested about. Thank you!

]]> By: felix http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-60609 felix Sat, 15 Jan 2011 00:17:24 +0000 http://www.johndcook.com/blog/?p=925#comment-60609 Of course, you can replace isOdd(p) by p != 2. The semantics of the resulting program don't change (assuming correct input), i.e. it does not really matter. There is a small difference, though: depending on how p is stored, isOdd(p) can be faster to determine than p != 2. Of course, you can replace isOdd(p) by p != 2. The semantics of the resulting program don’t change (assuming correct input), i.e. it does not really matter.
There is a small difference, though: depending on how p is stored, isOdd(p) can be faster to determine than p != 2.

]]> By: Zoresvit http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-60599 Zoresvit Fri, 14 Jan 2011 22:59:35 +0000 http://www.johndcook.com/blog/?p=925#comment-60599 As I understand we have pairs (p, n), where p — factor of our module, that is prime, n — it's power. Out of all prime numbers only 2 is even. Why not just check p if it equals 2 instead? Or it doesn't matter and was used for generality? As I understand we have pairs (p, n), where p — factor of our module, that is prime, n — it’s power. Out of all prime numbers only 2 is even. Why not just check p if it equals 2 instead? Or it doesn’t matter and was used for generality?

]]> By: John http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-36717 John Wed, 21 Apr 2010 12:09:04 +0000 http://www.johndcook.com/blog/?p=925#comment-36717 Felix: Thanks. I fixed the bug you found. Felix: Thanks. I fixed the bug you found.

]]> By: felix http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-31540 felix Tue, 26 Jan 2010 01:54:39 +0000 http://www.johndcook.com/blog/?p=925#comment-31540 Hi John, I think there's a typo in the code: the second "isOdd( p )" in the function "s" should have been an "isOdd( n )" if I'm right. -Felix Hi John,
I think there’s a typo in the code: the second “isOdd( p )” in the function “s” should have been an “isOdd( n )” if I’m right.
-Felix

]]> By: Daniel Lemire http://www.johndcook.com/blog/2008/11/19/how-many-numbers-are-squares-mod-m/comment-page-1/#comment-9976 Daniel Lemire Thu, 20 Nov 2008 06:19:06 +0000 http://www.johndcook.com/blog/?p=925#comment-9976 Well. In computers, we use fixed-length integers, especially if we want speed. You have either 32 bits or 64 bits. So your statement is false (from a computer programming point of view). We can always tell whether a number is a square from the 32 or 64 bits... ;-) This is not just a common routine, this is a fundamental part of our CPU architecture (which is register-based). I find it fascinating that one integer out of 6 is a square. Well. In computers, we use fixed-length integers, especially if we want speed. You have either 32 bits or 64 bits. So your statement is false (from a computer programming point of view). We can always tell whether a number is a square from the 32 or 64 bits… ;-) This is not just a common routine, this is a fundamental part of our CPU architecture (which is register-based).

I find it fascinating that one integer out of 6 is a square.

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