Lesson plan
Integer-valued polynomial
In mathematics, an integer-valued polynomial (also known as a numerical polynomial) P(t) is a polynomial whose value P(n) is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true. For example, the polynomial : P(t) = \frac{1}{2} t^2 + \frac{1}{2} t=\frac{1}{2}t(t+1) takes on integer values whenever t is an integer. That is because one of t and t + 1 must be an even number. (The values this polynomial takes are the triangular numbers.) Integer-valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology.
Article summary
In mathematics, an integer-valued polynomial (also known as a numerical polynomial) P(t) is a polynomial whose value P(n) is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true. For example, the polynomial : P(t) = \frac{1}{2} t^2 + \frac{1}{2} t=\frac{1}{2}t(t+1) takes on integer values whenever t is an integer. That is because one of t and t + 1 must be an even number. (The values this polynomial takes are the triangular numbers.) Integer-valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.