Fibonacci numbers are integers in the series 1, 1, 2, 3, 5, 8, 13, ... where each additional term is the sum of the two preceding terms.

Find all integer solutions to the following equations:
(1) A²+B²+C²=D² where A, B and C are Fibonacci numbers, and D is any integer.
(2) A²+B²+C²+D²=E² where A, B, C, D and E are Fibonacci numbers.
(3) A²+B²+C²+D²+E²=F² where A, B, C, D, E and F are Fibonacci numbers.

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