How do you call the operation of counting the number of euclidian division until the denominator is lower than the remainder?

Question

I was looking for the minimum size of a base35 secret_key to be able to generate at least 1,000,000 secret key.

The result is 35*35*35*35 = 1500625

How do you call this operation of counting the number of euclidian division until the denominator is lower than the remainder ?

I think where you wrote "remainder" you mean "quotient" and where you write "quotient" you mean divisor. This is essentially an integer logarithm. — Thomas Andrews, Feb 07 '13 at 15:20

score 1 · Accepted Answer · answered Feb 07 '13 at 15:22

1

I don't think there is a special name, but in a formula this boils down to $$\left\lceil\frac{\ln 1000000}{\ln 35}\right\rceil=4.$$

answered Feb 07 '13 at 15:22

Hagen von Eitzen

I love it thanks. – Natim Feb 07 '13 at 15:23
35^x > 1000000 | log_b(35^x) > log_b(1000000) | x . log_b(35) > log_b(1000000) | x > log_b(1000000) / log_b(35) | x > 3.88... – Natim Feb 07 '13 at 18:12
So if we are 7 billions on the planet. If everybody knows 100 persons you can reach anybody in 5 hop. Great. Thank you for this demonstration. – Natim Feb 07 '13 at 18:17

1 Answers1