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From: alainverghote on 8 Jul 2010 13:49
Good evening,

We may find equations of form:
T^[n](x) = y^2+z^2 ,
Trinoms with integer coefficients, n,y,z positive integer.
[n] number of iterations of T(x) ;

Example: T(x) = x^2-8x+20
T^[1](x) = x^2-8x+20 = (x-4)^2 + 2^2
T^[2](x) = T(T(x)) = (x^2-8x+20)^2-8(x^2-8x+20)+20
= (x^2-8x+16)^2 + 2^2

Namely T(x) equal sum of two squares ,so its iterates
T(7) = 7^2-8*7+20 = 13 = 3^2+2^2
T^[2](3) = 29 = 5^2+2^2

Do you believe this may be of any interest?

Alain
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