A112090 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.

7, 11, 13, 15, 21, 31

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..6.

Crossrefs

Sequence in context: A172247 A374082 A172120 * A373673 A103487 A175811

Adjacent sequences: A112087 A112088 A112089 * A112091 A112092 A112093

Keyword

fini,full,nonn,nice

Author

Richard Stanley, Nov 29 2005

Status

approved