Remark. On the other hand, it is more or less known Zeckendorf's theorem
in [13], which states that every positive integer can be represented uniquely
as the sum of one or moreistinct d Fibonacci numbers in such a way that the
sum does not include two consecutive Fibonacci numbers. Such a sum is called
Zeckendorf representation and it is related to the Fibonacci coding of a positive
integer. Our results are completely dierent, because the number of terms
is reduced to at most two, and the sum in the representation of solutions is a
linear combination with rational coecients.