I would like to solve the following problem. Knowing two constants $C_1 >1$ and $C_2>1$, I am looking for a sequence of real numbers $y_1,\ldots,y_n$ all greater than 1, such that:
- $y_1 = C_1$
- $y_j = aj+b$ for $j=1,\ldots,n$
- $\prod_{j=1}^n y_j = C_2$
Is there a clever way to solve this ? Thanks.