MathDB

Let

R(x)

be a function that takes a natural number as input and returns a rectangle.

R(1)

is known to have integer side lengths. Let

p(x)

be the perimeter of

R(x)

and let

a(x)

be the area of

R(x)

. Suppose that

p(x+5)=6 p(x)

for all

x

in the domain of

R

and that

a(x+2)=12a(x)

for all

x> 6

in the domain of

R

. For

x \leq 6

a(x+1)=a(x)+2

. Suppose

p(16)=1296

, and let the side lengths of

R(11)

a

and

b

with

a\leq b

. Find the ordered pair

(a,b)

.
Proposed by Matthew Weiss

Problem Statement