proof

[the_outsider]

prove that the matrix defined by {A}ij = (i+j-1)^-1 is invertible and has an inverse whose entries are all integers.

[HallsofIvy]

prove that the matrix defined by {A}ij = (i+j-1)^-1 is invertible and has an inverse whose entries are all integers.

Have YOU tried anything at all on this? In particular have you written out the 2 by 2 and 3 by 3 versions of {A}ij?

I think you would find the 3 by 3 version especially interesting!