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edit approved Dec 2, 2015 at 1:28

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For forms of the form $Ax^d - By^d$ this seems to have been done by Bennett, Dummigan, and Wooley:

Bennett, M. A.(1-MI); Dummigan, N. P.(1-MI); Wooley, T. D.(1-MI)
The representation of integers by binary additive forms. (English summary) 
Compositio Math. 111 (1998), no. 1, 15–33. 
11D85 (11D41 11P05)

M. A. Bennett, N. P. Dummigan, and T. D. Wooley, The representation of integers by binary additive forms, Compositio Math. 111 (1998), no. 1, 15--33.

For forms of the form $Ax^d - By^d$ this seems to have been done by Bennett, Dummigan, and Wooley:

Bennett, M. A.(1-MI); Dummigan, N. P.(1-MI); Wooley, T. D.(1-MI)
The representation of integers by binary additive forms. (English summary) 
Compositio Math. 111 (1998), no. 1, 15–33. 
11D85 (11D41 11P05)

For forms of the form $Ax^d - By^d$ this seems to have been done by Bennett, Dummigan, and Wooley:

M. A. Bennett, N. P. Dummigan, and T. D. Wooley, The representation of integers by binary additive forms, Compositio Math. 111 (1998), no. 1, 15--33.

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created Oct 2, 2015 at 22:05

Igor Rivin

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For forms of the form $Ax^d - By^d$ this seems to have been done by Bennett, Dummigan, and Wooley:

Bennett, M. A.(1-MI); Dummigan, N. P.(1-MI); Wooley, T. D.(1-MI)
The representation of integers by binary additive forms. (English summary) 
Compositio Math. 111 (1998), no. 1, 15–33. 
11D85 (11D41 11P05)