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• Woh! Steady on, Jon. You re _way_ off base here. 2 is not coprime to 30. gcd(2,30)=2 3 is not coprime to 30. gcd(3,30)=3 5 is not coprime to 30. gcd(5,30)=5 1
Message 1 of 5 , Mar 1, 2003
'Woh! Steady on, Jon. You're _way_ off base here.

2 is not coprime to 30. gcd(2,30)=2
3 is not coprime to 30. gcd(3,30)=3
5 is not coprime to 30. gcd(5,30)=5

1 is coprime to 30. gcd(1,30)=1

|{1,7,11,13,17,19,23,29}| = 8 as correctly stated by Liu.'

Correct. As the whole page in question
(http://www.primepuzzles.net/problems/prob_037.htm) is completely littered
with typos and misleading nomenclature, I don't feel completely aggrieved at
having made such a simple error.

As to what 'Tn mod mn is equivalent to the class of residues
Tn+<0,1,2,...,pn=1>*<mn> mod m[n+1]'

T_n mod m_n is equivalent to the class of residues
Tn+(<0,1,2,...,pn-1>*<mn>) mod m_(n+1)

which comes clear if you look at the examples, except for m_n is incorrectly
defined.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• Thanks a lot for your responses. What I am confused about is that I don t understand how adding * to Tn makes it equivalent mod m[n+1].
Message 2 of 5 , Mar 1, 2003
Thanks a lot for your responses. What I am confused about is that I
don't understand how adding <0,1,2,...,pn-1>*<mn> to Tn makes it
equivalent mod m[n+1]. What I would like is a theorem like the one
that one can uset to prove that if (k,S)=1 and S is a reduced
residue system then so is k*S. I think it should be obvious since
most people accept it and I see from examples that it is true, but I
just want to know what theorem he is using to imply this equivalence
or if it follows directly from the definition of Tn. Any help will
be greatly appreciated.
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