1. Hello there!

I didn't manage to solve a specific math riddle (anyway, i'm not a maths freak), maybe you can, so here it is:

where you can notice that:
An=n
Cn=An+Bn
Σ Cn= Σ odd Cn + Σ even Cn

The "odd Cn" and "even Cn" columns must be filled respectively with odd results of An+Bn and even results of An+Bn

For instance: If the result of A6+B6 is even, place the result in "Even Cn" column in the 6th line, and you put a 0 at the "Odd Cn" column in the same line.
if the result is odd, it's the other way round.

Warning: An, Bn and Cn are natural numbers (zero is excluded)!
And the result of Σ odd Cn must be also an odd number.

Accepting these instructions, how do you proceed to replace B1, B2, B3, ect.. with number (and fixing "n max") in such manner we get
ΣAn= Σ odd Cn and ΣBn= Σ even Cn
at the same time?

Good luck!

2.

3. If we define the relationship you wrote as the following:

Than all even c_n can be expressed in the following manner:

Similarily, the definition of all odd c_n would be the following:

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