1. ## Ramanujan

2. Hi. You asked to solve one such system for the values you gave and I tried to think of the most compact way of doing so in Mathematica:

Code:
coeff = {2, 3, 4, 6, 12, 32};
mycoeff = Table[Subscript[a, n] ->
coeff[[n]], {n, 1, 6}];
myvars = Join[Table[Subscript[x, n],
{n, 1, 3}], Table[Subscript[y, n],
{n, 1, 3}]];
myequations = Table[
Sum[Subscript[x, j]*Subscript[y, j]^
(n - 1), {j, 1, 3}] ==
Subscript[a, n], {n, 1, 6}];
Solve[myequations /. mycoeff, myvars]
which returns six sets of solutions.

3. Thanks for your reply. I didn't think at PC program for solving; such sistems are actuel in code theory and Ramanujan discavered method (in 1913) of solving such sistems. This is what I'm interesting.

Update:O my God, I have a book in which this stuff is considered. So, here I will share this with poeple. Languge is russian, but it doesn't metter to much

I hope somebody will find this Ramanujan's paper in english.
And I findet what is neccessary

http://www.ams.org/bookstore-getitem/item=CHEL/159.H

and here is another one

http://bmf.hu/conferences/cinti2007/18_DombiJozsef.pdf

Well, maybe it was better that I post this in Web-room.

and here you can see this paper at