  CTK Exchange Front Page Movie shortcuts Personal info Awards Reciprocal links Privacy Policy Cut The Knot! MSET99 Talk Games & Puzzles Arithmetic/Algebra Geometry Probability Eye Opener Analog Gadgets Inventor's Paradox Did you know?... Proofs Math as Language Things Impossible My Logo Math Poll Other Math sit's Guest book News sit's |Store|      CTK Exchange

 Subject: "RE: Chinese Remainder Problem - a =..." Previous Topic | Next Topic
 Conferences The CTK Exchange College math Topic #80 Printer-friendly copy Email this topic to a friend Reading Topic #80
Steve Brown (Guest) guest
Mar-30-01, 08:45 AM (EST)

"RE: Chinese Remainder Problem - a = b (mod 1) ?"

 on https://www.cut-the-knot.com/blue/chinese.shtmlit'states:When m1 and m2 are coprime their gcd is 1. By convention, a = b (mod 1) is simply understood as the usual equality a = b.What strikes me as odd is the phrase "is simply understoodas the usual equality a = b"...if I understand correctly 'a' and 'b' may not be equal!i.e. 3 = 5 (mod 1) does not mean that 3 = 5.Am I understanding 'mod' correctly?.Consider:n = 3 (mod 27)n = 5 (mod 25)Chinese remainder Theorem states this has a solution iff3 = 5 (mod 1), since gcd(25,27)=1a = b (mod 1) should aways be true yes? (since a (mod1) = 0 and b (mod 1) = 0) ?In this case it would seem Chinese Remainder Theorem isreally only useful if gcd(m1,m2) > 1 otherwise it doesn'treally help you find n1 or n2, (or n).(The solution for the above is n=30)Steve

alexb
Charter Member
672 posts
Mar-31-01, 01:17 AM (EST)    1. "RE: Chinese Remainder Problem - a = b (mod 1) ?"
In response to message #0

 LAST EDITED ON Mar-31-01 AT 01:18 AM (EST)Steve, many thanks for your note. That statement is just plain wrong.The congruence a = b (mod m) is equivalent to existence of integer t such that a = b + tm. If m = 1, this is true for any a and b (t being just the difference a - b.)My apologies. Probably wrote that stupid remark much past midnight.What is true is that a = b (mod 0) is equivalent to the customary a = b. But this is quite irrelevant in the context of the CRT.Thank you again,Alexander Bogomolny Steve Brown (Guest) guest
Mar-31-01, 09:10 AM (EST)

2. "RE: Chinese Remainder Problem - a = b (mod 1) ?"
In response to message #1

 Hi Alexander,Thanks for the quick reply!Great website BTW.Regards,Steve

 Conferences | Forums | Topics | Previous Topic | Next Topic
 Select another forum or conference Lobby The CTK Exchange (Conference)   |--Early math (Public)   |--Middle school (Public)   |--High school (Public)   |--College math (Public)   |--This and that (Public)   |--Guest book (Public) You may be curious to visit the old CTK Exchange archive.    