Equal fractions

[Genady]

5 hours ago, studiot said:

factorise 2⁴⁸⁴  +  1

I got one factor. 17.

[studiot]

1 hour ago, Genady said:

I got one factor. 17.

yes starting with the shortest one is good.

[Genady]

1 hour ago, studiot said:

the shortest [factor]

What do you mean? Number of digits?

[studiot]

13 minutes ago, Genady said:

What do you mean? Number of digits?

Yes 17 is the only 2 digit factor (in decimal)

The next one is 3 digits and the one after that 6 digits.

[Genady]

11 hours ago, studiot said:

Yes 17 is the only 2 digit factor (in decimal)

The next one is 3 digits and the one after that 6 digits.

Thank you.

I don't have any progress to report on my part, but would ask you to clarify your answers somewhat (to get a hint, maybe):

Do you mean 3-digits and 6-digits prime numbers?

There are more than these three factors, aren't there? (Only these three fall short of 2⁴⁸⁴.) Or, do you mean these three just repeat many times in the factorization?

[studiot]

1 hour ago, Genady said:

Thank you.

I don't have any progress to report on my part, but would ask you to clarify your answers somewhat (to get a hint, maybe):

Do you mean 3-digits and 6-digits prime numbers?

There are more than these three factors, aren't there? (Only these three fall short of 2⁴⁸⁴.) Or, do you mean these three just repeat many times in the factorization?

It's not a trick question, its designed to test the limits of computers.

Wolfram Alpha gave up when I asked it.

 

There are 7 factors, all different.

One of them is very large itself.

Of course they are all prime. Isn't that a requirement for factors ?

The second one is 353

[Genady]

4 minutes ago, studiot said:

its designed to test the limits of computers

Oh. I found the first one with pen and paper.

[studiot]

25 minutes ago, Genady said:

Oh. I found the first one with pen and paper.

It's the sort of thing that is being studied in what's called  (Higher) Arithmetic  these days.

 

The Higher Arithmetic

Davenport

 

Cambridge university press