4

Part of 1987 ITAMO

Problems(1)

I_n is set of solutions x^2 −2xy+y^2−4^n = 0 , where y \in I_{n-1}

Source: ITAMO 1987 p4

I_0 = \{-1,1\}

I_n

recurrently as the set of solutions

x

of the equations

x^2 -2xy+y^2- 4^n = 0

y

ranges over all elements of

I_{n-1}

. Determine the union of the sets

I_n

over all nonnegative integers

n

equationSetsalgebra