**To: The America Mathematical Society**
**
Attn.: Mr. Clifford J Earle, the Managing Editor**
**
Fm: Li Ke Xiong**
**
Email: likexiong@126.com**

Dear Mr. Clifford J Earle,

I received your letter dated 8 July, many thanks.

I think, I can and I should answer your questions, let me explain one by
one.

A. (1) I think you have already read ------

" The Supplement of the Development of the Concept
of Congruence" written by

me.

In this supplement, we have got the " Theorem A' ": For any P ,

And we have checked the Theorem A' with real example p=3,5,7 and 11 in
our

paper, everything is OK. If necessary, I can go on our checking, I deeply
believe

our Theorem A' is correct. We have discovered the " structure " of ,

for example again:

please
note if

so the above

thus ------
this is our way.

Let us put it in common way:

we can see

It is obvious the content of the two ways are totally different, though
the result are

the same.

(2) Theorem A is the direct result from Theorem A'.

according
to our theory, we should calculate

to see if
Maybe the calculation should depend on bigger

computer. Though we believe our Theorem A' is right and should have

we
will try our best to work it out really. [Actually, when

n=273, that is 546/2, we can say the sum of 1/n (n from 1 to 273) congruent
0.

mod p]

(3) I think, it's more convenient for you to use some bigger computer to
check our

theory, if you are willing to do so, we thank you in advance.

B. About the example on page 4 of our paper, you are right, sorry, it's
my

careless. We should set p>3, thus everything will be OK. Actually, this
is

" Wolstenholme Theorem ", we merely use our theory to re-prove it,
just as a test

for our theory.

C. About the Part B of my definition, we totally accept your advice. The
sentence

" Will have certain meanings " should be changed. We should use " the

congruent " instead of " certain ", to avoid vagueness.

D. According to our Definition I (B) on page 3: Never can " p " be as the

denominator divisor of any finite expression, otherwise meaningless, we
re-write

our Theorem B(1) on page 4 as follows:

integers k, m, q, s.

Thank you for your precious directions, many many thanks from my heart.
Please

continue with your precious instructions, let's make new discovery together.

Best Regards

Li Kexiong, July 18th, 1999

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Email: likexiong@126.com

Update Time: 99/08/01

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