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The Homflypt and Kauffman skein modules of the projective space are computed. Both are free and generated by some infinite set of links. This set may be chosen to be {Lₙ: n ∈ ℕ ∪ {0}}, where Lₙ is an arbitrary link consisting of n projective lines for n > 0, and L₀ is an affine unknot.
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