A240775 The six values n in each interval [i*840, (i+1)*840), where i >= 0, for which Mordell's formulas do NOT provide a three-Egyptian-fraction solution for 4/n.

1, 121, 169, 289, 361, 529

Offset: 1

Author

Kenneth Vollmar, Apr 12 2014

Keywords

• nonn
• fini
• full

Comments

Erdős and Straus conjectured that for all integers n >= 2, the rational number 4/n can be expressed as an Egyptian fraction with exactly three unit fractions -- that is, 4/n = 1/x + 1/y + 1/z where x, y and z are positive integers. The conjecture has been verified to high values of n, and Mordell has provided formulas to compute x, y and z for many n. The values of n NOT included in Mordell's formulas are those for which n modulo 840 = {an element of this sequence}. Each element is the square of a prime.

References

• Louis J. Mordell, Diophantine Equations, Academic Press, 1967, 287-290.