Integer-Representing Polynomial

A polynomial that represents integers for all integer values of the variables. An integer polynomial is a special case of such a polynomial. In general, every integer representing polynomial f(x) of degree n in the variable x can be written in the form

 f(x)=A_0+A_1(x; 1)+A_2(x; 2)+...+A_n(x; n),

where (n; k) is a binomial coefficient and A_0, A_1, ..., A_n are integers (Nagell 1951, p. 121).

See also

Integer Polynomial

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Nagell, T. "Polynomials Representing Integers." §35 in Introduction to Number Theory. New York: Wiley, pp. 115-120 and 121, 1951.

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Integer-Representing Polynomial

Cite this as:

Weisstein, Eric W. "Integer-Representing Polynomial." From MathWorld--A Wolfram Web Resource.

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