On a test of the modified BCS theory performance in the picket fence model

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The errors in the arguments, numerical results, and conclusions in the paper "Test of a modified BCS theory performance in the picket fence model" [Nucl. Phys. A 822 (2009) 1] by V.Yu. Ponomarev and A.I. Vdovin are pointed out. Its repetitions of already published material are also discussed.
This version updates Ref. [9] and corrects a typo in Eq. (3)

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