'Suppose that: the Tn is a complete set of residues prime to mn, the least

number more than 1 in this set U(Tn) is the n-th prime pn. The number of

elements of the set Tn is | Tn |=(p1-1)*(P2-1)*...*(p[n-1]-1). If p>p[n-1]

is a prime, then p belongs the class of residues Tn mod mn.'

I don't get this. mn is defined as "Let mn=p0*p1*...p[n-1]", therefore

m2=2.3=6 and m3=2.3.5=30

However, the number of residues prime to 30 is

|{2,3,5,7,11,13,17,19,23,29}|=10, and not the 8 predicted by Liu. I suppose

the p>3 property comes into play...

'If p>p[n-1] is a prime, then p belongs the class of residues Tn mod mn.'

Suppose p is a prime and p doesn't belong to tmod30, this is impossible.

Induction carries on from here.

I think what '"...the class of residues Tn mod mn is equivalent to the class

of

residues Tn+<0,1,2,...,pn=1>*<mn> mod m[n+1],"'

means is that we are looking at either (pn,mn)=1 OR (tn+pn,mn)=1.

HTH

Jon Perry

perry@...
http://www.users.globalnet.co.uk/~perry/maths/
http://www.users.globalnet.co.uk/~perry/DIVMenu/
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-----Original Message-----

From: velozant <

velozant@...> [mailto:

velozant@...]

Sent: 28 February 2003 22:15

To:

primenumbers@yahoogroups.com
Subject: [PrimeNumbers] reduced residue systems question please help

I was looking at

http://www.primepuzzles.net/problems/prob_037.htm
and in the proof of the formula mr Fengsui claims that

"...the class of residues Tn mod mn is equivalent to the class of

residues Tn+<0,1,2,...,pn=1>*<mn> mod m[n+1],"

could anyone explain to me in simple terms why this is?

any help will be greatly appreciated. have a good day.

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