MathDB

There is a unique choice of positive integers

a

b

, and

c

such that

c

is not divisible by the square of any prime and the infinite sums \sum_{n=0}^{\infty} \left(\left(\frac{a - b\sqrt{c}}{10}\right)^{n-10}\cdot\prod_{k=0}^{9} (n - k)\right) \text{and} \sum_{n=0}^{\infty} \left((a - b\sqrt{c})^{n+1}\cdot\prod_{k=0}^{9} (n - k)\right) are equal (i.e., converging to the same finite value). Compute

a + b + c

Problem Statement