Equivalence of two sets of Hamiltonians associated with the rational Ruijsenaars-Schneider-van Diejen system
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Two families of first integrals of van Diejen's rational BC(n) system are considered.

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Equivalence of these two complete sets of Poisson commuting Hamiltonians is proved.

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Van Diejen's Hamiltonians depend linearly on those generated by Pusztai's Lax matrix.

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The explicit formula of this invertible linear relation is found.

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