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Degrees of nonconstant complex polynomials f(x) and g(x) such that (1) neither f nor g can be written nontrivially as r(s(x)), (2) f(x) does not equal g(ax+b) for complex numbers a,b and (3) f(x)-g(y) is reducible as a complex polynomial in two variables.

There are no further terms. The proof of this statement uses the classification of finite simple groups.

REFERENCES

J. W. S. Cassels, Factorization of polynomials in several variables, Proc. Fifteenth Scandinavian Congress (Oslo, 1968), vol. 118, Lecture Notes in Mathematics, Springer, Berlin, pp. 1-17.

W. Feit, Some consequences of the classification of finite simple groups, in The Santa Cruz Conference on Finite Simple Groups, Proc. Sympos. Pure Math. 37, American Mathematical Society, 1980, pp. 175-181.