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We prove a conjecture of Helleseth that claims that for any $n \geq 0$, apair of binary maximal linear sequences of period $2^{2^n}-1$ can not have athree-valued cross-correlation function.

Proof of a Conjecture of Helleseth: Maximal Linear Recursive Sequences of Period $2^{2^n}-1$ Never Have Three-Valued Cross-Correlation