5-Mar-1995
Unsolved Problem 10:
If n is an integer larger than 1, must there be
integers x, y, and z, such that 4/n=1/x+1/y+1/z?
A number of the form 1/x where x is an integer
is called an Egyptian fraction.
Thus, we want to know if 4/n is always the sum
of three Egyptian fractions, for n>1.
Reference:
- [Erdos 1980]
- Paul Erdös and Ronald L. Graham,
Old and New Problems and Results
in Combinatorial Number Theory.
L'Enseignement Mathématique. Geneva, Switzerland: 1980.
Page 44.
Egyptian Fractions
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