Same when writing "d" instead of "N" ...
But when writing
Exp[-x]^(d - n)*Exp[x]^n
instead of
Exp[(2n - d)x]
it works (see bug2.nb attached)
Edit:
Writing Exp[-x (d - n)] Exp[x n] , which is also the same (or not ??) as Exp[-x]^(d - n)*Exp[x]^n does not work too...
any idea why the identities [ x^a * x^b == x^(a+b) ] and [ (x^a)^b == x^(a*b) ] (which are essentially the same) are not used in FullSimplify when assuming "d" from above to be an Integer ??
Edit2:
Even more interesting is, that " Exp[(2n - d)x] - Exp[-x]^(d - n)*Exp[x]^n // FullSimplify " gives 0 (as it should) with both assumptions (see bug3.nb).
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