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Abstract  In a recent paper by Das, Laishram and Saradha, it was shown that if there exists a rational solution ofy  l   =   (  x  +  1  )   …   (  x  +  i  −  1  )    (  x  +  i  +  1  )   …   (  x  +  k  )for   i   not too close to    k  /  2    and    y  ≠  0   , then    log    l  <   3  k    . In this paper, we extend the number of terms that can be missing in the equation and remove the condition on   i  .

On a variation of the Erdős–Selfridge superelliptic curve