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From: alainverghote on 12 Jul 2010 13:00
Good afternoon,

Some years ago while working with iterates I fell upon :
T[n+1](x) +(r1-r2)^2/4 = (T^[n](x) - (r1+r2)/2 )^2

T(x) a trinom (x-r1)*(x-r2) , T^[n](x) its nth iterate ,

Example:
T(x) = (x-2)*(x-4) = x^2-6x+8
T^[2](x) = (x^2-6x+8-2)*(x^2-6x+8-4) = (x^2-6x+5)^2 - 1

When r1 and r2 same parity,
T^[2](x) is a difference of two squares,

Alain
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