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Polynomials which are near to k-th powers

Published online by Cambridge University Press:  24 October 2008

K. R. Matthews
Affiliation:
Trinity College, Cambridge

Extract

1. Let f(x) be a polynomial of degree n ≥ 2 with integral coefficients, the highest coefficient being positive. It is well known that if f(x) is an exact k-th power for all sufficiently large integers x, where k ≥ 2, then f(x) = g(x)k identically, where g(x) is another polynomial with integral coefficients. (See Pólya and Szegö (4), section 8, problems 114, 190; also Davenport, Lewis and Schinzel(1), where other references are given.) The main purpose of this note is to prove that if we suppose only that

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

REFERENCES

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