# Homework Help: 68068 as difference of two squares

1. Nov 2, 2014

### Robert Houdart

1. The problem statement, all variables and given/known data
In how many ways can 68068 be written as the difference of two squares?

2. Relevant equations

3. The attempt at a solution
Let (x+a) * (x+a) -x*x =68068=2*2*7*11*13*17
a (2x+a) =2*2*7*11*13*17
As 2x+a is odd ⇒ a is even
∴a=2b
2b (2x+2b) =2*2*7*11*13*17
b (x+b) =7*11*13*17
x= (7*11*13*17) /b - b
Since 7*11*13*17 has 16 factors ∴ x has 16 different values
However, the book states 8 as the answer.

2. Nov 2, 2014

### RUber

It looks like you need to account for the pairs (x,b) (b,x) , since those would not be distinct differences of squares.

3. Nov 2, 2014

### Robert Houdart

i
I guess you are right. (a, b) and (b, a) are repeated in my solution, taking pair (a,b) and (b,a) as a single pair yields 8 as the answer.

4. Nov 2, 2014

### PeroK

That's not quite the reason. Remember that you had factors b and x+b. That implies a constraint.