Polynomial identities listed by Mordell provide three-term Egyptian fractions for whenever is mod (above), mod , or mod , , , or mod , or mod 8. The other cases modulo 8 of , , and mod are already covered by earlier identities. These identities cover all the numbers that are not quadratic residues for those bases. However, for larger bases, not all nonresidues are known to be covered by relations of this type. From Mordell's identities one can conclude that there exists a solution for all except possibly those that are , , , , , or modulo . is the smallest prime number that is not covered by this system of congruences. By combining larger classes of modular identities, Webb and others showed that the fraction of in the interval that can be counterexamples to the conjecture tends to zero in the limit as goes to infinity.