MathDB

And if you interchange the digits...

Source: 1st German pre-TST 2006, problem 3

December 5, 2005

modular arithmeticnumber theory proposednumber theory

Problem Statement

Is the following statement true? For each positive integer

n

, we can find eight nonnegative integers

a

b

c

d

e

f

g

h

such that

n=\frac{2^a-2^b}{2^c-2^d}\cdot\frac{2^e-2^f}{2^g-2^h}