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Bauer's Theorem

Bauer's theorem guarantees infinitely many prime divisors not congruent to 1 modulo m for an integer polynomial with a real root. Let m>=3 be an integer and let

f(x)=sum_(k=0)^na_kx^(n-k)

be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not congruent to 1 (mod m) (Nagell 1951, p. 168).

See also

Bauer's Identical Congruence, Prime Divisor

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References

Nagell, T. "A Theorem of Bauer on the Prime Divisors of Certain Polynomials." §49 in Introduction to Number Theory. New York: Wiley, pp. 168-169, 1951.

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Bauer's Theorem

Cite this as:

Weisstein, Eric W. "Bauer's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BauersTheorem.html

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