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Geometric progression. The denominator and the first term

Finding the denominator and the first term the integral geometric progression for two adjacent terms.

The site already has a calculator for of a geometric progression- Geometric progression, which allows you to find the sum of its terms. However, there is also another task - for two adjacent terms if geometric progression to find denominator and its first term.It is clear that in such formulation of the problem we are talking about increasing geometric progression, the first member of which, as well as the denominator are integers.

It's all clear with denominator, two adjacent terms of geometric progression are related
a_n=a_{n-1}q,
whence
q=\frac{a_n}{a_{n-1}}

But to get the first term, we should decide every previous one by q, until we won't have integers.
Last integer and will be the first member of a geometric progression. Actually, I've made calculator below so you won't get tired with all this division.

PLANETCALC, Geometric progression. The denominator and the first term

Geometric progression. The denominator and the first term

First term of a geometric progression
 
Denominator of a geometric progression
 

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