TOPICS
Search

Bauer's Theorem


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

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Bauer's Theorem

Cite this as:

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

Subject classifications