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Express uniqueness: every positive integer n can be written as k*2^m with k odd,...

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Express uniqueness: every positive integer n can be written as k*2^m with k odd, uniquely. Which logical form captures uniqueness?

∃k∃m (k odd ∧ n=k*2^m ∧ ∀k'∀m'(n=k'*2^{m'} → k'=k ∧ m'=m))

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∀k∃m (k odd ∧ n=k*2^m ∧ ∀k'∀m'(n=k'*2^{m'} → k'=k ∧ m'=m))

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∃k∀m (k odd ∧ n=k*2^m ∧ ∀k'∀m'(n=k'*2^{m'} → k'=k ∧ m'=m))

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∃k∃m (n=k*2^m)

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