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I know of six solutions: {4,5,6,7,8,9}
Consider this equation as base^exponent = 1
The exponent is (x-8)(x-9), so two solutions are 8 and 9, because anything (except zero) to the zero power is 1.
The base can be written as
(x-4)(x-7)+1 and therefore solutions 4 and 7 make the base equal to 1. One to any power equals 1.
The base can also be written as
(x-5)(x-6)-1 and therefore solutions 4 and 7 make the base equal to -1 and in each of these cases the exponent will be an even number. And -1 to an even power equals 1.
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