Math Is Fun Forum

jacks

Member

Registered: 2012-11-21

Posts: 132

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

(1) If

Then value of

is

(2) If

. Then value of

is

Last edited by jacks (2013-10-13 16:49:37)

jacks

Member

Registered: 2012-11-21

Posts: 132

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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

You mean

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

4, actually.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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 (2013-10-13 21:07:18)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

Compare these two:

34!=295232799cd9604140847618609ab0000000

34!=295232799039604140847618609643520000000

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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...

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

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

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

Found only this:http://forum.math.uoa.gr/viewtopic.php?f=37&p=211113 which suggests that your answer is still the correct one.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

zetafunc.

Guest

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

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

Ah, thanks. Found it:

http://www.bmoc.maths.org/home/bmomarking.pdf

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.