What would be the base a given number should be in to represent certain number in another base?

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I need to find a base in order to have the same number represented in two different bases. For example, given 16947800 and 2372452, find a base b so that 16947800=2372452b

What I have tried:

The definition of a base, but that involves solving a polynomial equation of increasing degree, which proves too compute-intensive.

Posted 12-May-18 14:08pm

SACC92

Updated 12-May-18 14:43pm

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Patrice T · Accepted Answer · 2018-05-12T14:44:00

Solution 1

Quote:
I need to find a base in order to have the same number represented in two different bases. For example, given 16947800 and 2372452, find a base b so that 16947800=2372452b

Why don't you try every possible bases ?
It take 16947800 and covert to the base you test.

Quote:
The definition of a base, but that involves solving a polynomial equation of increasing degree, which proves too compute-intensive.

What operation need 'solving a polynomial equation' ?

Posted 12-May-18 14:44pm

Patrice T

Updated 12-May-18 22:06pm

v4

Comments

SACC92 13-May-18 15:47pm

I would need to convert very large numbers, of order 10^18, but your suggestion is actually helpful, as I was thinking the other way around, as in, take base b, then solve the equation, in this example, 2*b^6 + 3*b^5 + 7*b^4 + ... + 2 = 16947800. Your approach, as in doing it the other way around, seems far more effective. Do you think doing a search for the base with some sort of bisection algorithm for the base interval would work for large numbers as the ones I'll need to work with?

Patrice T 13-May-18 16:00pm

My first approach is brut force, there is not so many bases to check.
If bases are between 10 and 500, dichotomy is ok.
Here, there is just a few bases to check.