Egyptian fraction

The calculation of Mᴺ where both M and N are real numbers can be done by expressing N as the sum of an integer h and an Egyptian fraction 1#47;g#95;1#43;1#47;g#95;2#43;1#47;g#95;3#43;.... Then Mᴺ#61;Mʰ#92;sqrt#91;g#95;1#93;#123;M#125;#92;sqrt#91;g#95;2#93;#123;M#125;#92;sqrt#91;g#95;3#93;#123;M#125;... where each of the roots can be calculated by means of the Newton–Raphson method.

1995, C. Pomerance, A. Sárkőzy, Combinatorial number theory, R. L. Graham, M. Grötschel, L. Lovász (edtors), Handbook of Combinatorics, Elsevier (North-Holland), page 1014, However, a representation of r as a sum of distinct Egyptian fractions is certainly not unique and this fact leads to many questions.