1

Part of 2003 Putnam

Problems(2)

Source:

n

be a fixed positive integer. How many ways are there to write

n

as a sum of positive integers,

n = a_1 + a_2 + \cdots a_k

k

an arbitrary positive integer and

a_1 \le a_2 \le \cdots \le a_k \le a_1 + 1

? For example, with

n = 4

, there are four ways:

4

2 + 2

1 + 1 + 2

1 + 1 + 1 + 1

PutnamLaTeXinequalitiesalgorithmfloor functioncollege contestspartition

Source:

Do there exist polynomials

a(x)

b(x)

c(y)

d(y)

1 + xy + x^2y^2= a(x)c(y) + b(x)d(y)

holds identically?

Putnamalgebrapolynomiallinear algebramatrixfunctionvector