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## #1 2013-10-14 15:47:11

jacks
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### calculation of (a,b,c,d) in 34!

(1) If

Then value of
is

(2) If
. Then value of
is

Last edited by jacks (2013-10-14 15:49:37)

## #2 2013-10-14 15:53:39

jacks
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### Re: calculation of (a,b,c,d) in 34!

I have solved (1) one

19! contain factor of 9. so R.H.S must be divisible by 9.

So for divisibility by 9., sum of digit must be divisible by 9.

So

so a = 1 .

But I did not understand how can i solved (ii) one

Thanks

## #3 2013-10-14 19:05:39

anonimnystefy
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### Re: calculation of (a,b,c,d) in 34!

Hi jacks

There are a few thing you will need to do there. First, you should find the number of 0's with which 34! ends. You will find out that both a and b are 0. Then you use divisibility by 9 and 27 to get c and d.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #4 2013-10-14 19:07:38

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

Hi;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #5 2013-10-14 19:14:13

anonimnystefy
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### Re: calculation of (a,b,c,d) in 34!

Hi bobbym

I did it of the top of my head and I remember a similar problem where the answer was found the way I described above, so I just guessed that was it. Looks like I'll have ti have a bit more thinking.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #6 2013-10-14 19:15:46

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

Hi;

I am not seeing any quick way for either pair, are you?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #7 2013-10-14 19:33:08

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

I thought about using 4 divisibility rules, but I do not think that will do much.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #8 2013-10-14 19:35:43

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

If we could get 4 congruences that could be solved with the CRT. I just do not see how.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #9 2013-10-14 19:38:39

anonimnystefy
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### Re: calculation of (a,b,c,d) in 34!

Well a+b+c+d:7 (mod 9). And we can easily calculate it mod 11.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #10 2013-10-14 19:44:07

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

You mean

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #11 2013-10-14 19:48:45

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

4, actually.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #12 2013-10-14 20:02:26

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

The numbers are 0, 3, 5, 2 which sum to 10. Which is 1 mod 9.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #13 2013-10-14 20:06:56

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

Actually, the problen is that there are 3 digits missing in post #1. ab basically stsnds for 64352 in that number.

Last edited by anonimnystefy (2013-10-14 20:07:18)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #14 2013-10-14 22:58:05

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

I am not following you.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #15 2013-10-14 23:18:37

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

Compare these two:

34!=295232799cd9604140847618609ab0000000

34!=295232799039604140847618609643520000000

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #16 2013-10-14 23:21:01

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

That is true, I did not notice that.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #17 2013-10-15 01:12:20

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

I guess we'll have to wait for the OP to clear the question out.

But, either way, if it were like we initially thought, I don't know how we can get the answer...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #18 2013-10-15 01:18:59

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

Hi;

I agree, I do not even have a question like that in my notes and an internet search came up dry.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #19 2013-10-15 01:51:17

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

I've seen a similar one with 28!, but not this one.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #20 2013-10-15 01:53:15

anonimnystefy
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### Re: calculation of (a,b,c,d) in 34!

Found only this:http://forum.math.uoa.gr/viewtopic.php? … p;p=211113 which suggests that your answer is still the correct one.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #21 2013-10-15 01:56:11

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

That post is like 3 years old but has the same username!

See you later am going offline for a bit.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #22 2013-10-15 02:00:17

anonimnystefy
Real Member

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### Re: calculation of (a,b,c,d) in 34!

Hi

This one also turned up:http://mathforum.numberempire.com/index.php?topic=709.0. It's a bit more recent.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #23 2013-10-15 08:07:28

zetafunc.
Guest

### Re: calculation of (a,b,c,d) in 34!

I remember doing this question in a BMO1 paper, I think.

## #24 2013-10-15 08:19:41

anonimnystefy
Real Member

Offline

### Re: calculation of (a,b,c,d) in 34!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #25 2013-10-15 09:59:10

bobbym

Online

### Re: calculation of (a,b,c,d) in 34!

Hi;

I thought that they would not want any modulo-computation methods so I did not use them.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.