[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 272

New comment
 

Prove that there is a number that is divisible by 5^1000 and does not contain any zeros in its notation. 88

 

Five and one?

 

Meaning?

 

5/5^1000 и 1/5^1000.


Oh, and also 5^1000/5^1000.

 

Swetten, it must be an integer that is divisible by a huge 5^1000 without a remainder (i.e. it must be even larger than 5^1000). And it must not have a single zero - neither at the end, nor somewhere in the middle.

 

Then (5^1000)^2. No?

 

Prove that there are no zeros in his decimal notation. I don't know yet myself.

 

I swear I don't!!! :)


I smell a catch, but I can't substantiate it.

 

I remember from school that if you multiply A's, then... That's what, I don't remember.


P.S. Or odd numbers in general?

 

Here's the row:


5

25

625

3125

15625

78125

390625


Simply by probability theory, this number does not have zeros.

1...265266267268269270271272273274275276277278279...628
New comment