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Find A,B,C and D as integers such that

[tex] (3*2^{.75} + 7*2^{.50} + 7*2^{.25} + 7)*(A*2^{.75} + B*2^{.50} + C*2^{.25} + D) = 2047*(2^{.75} + 2^{.50} +2^{.25} + 1) [/tex].

I deduced this by studying the recursive sequence [tex]S^{n} = 3*S_{n-1} - 2*S_{n-2}[/tex] That is {1,3,7,15,31, ...}

Thanks for any pointers.