MathDB

TOT 338 1992 Spring A S6 no of decompositions in product of integers

Source:

June 9, 2024

number theorycombinatorics

Problem Statement

For natural numbers

n

and

b

, let

V(n, b)

denote the number of decompositions of

n

into the product of integers each of which is greater than

b

: for example

36 = 6\times 6 = 4\times 9 = 3\times 3\times 4 = 3\times 12,

i.e.

V(36,2) = 5

. Prove that

V(n, b) < n/b

for all

n

and

b

.
(N.B. Vasiliev, Moscow)