When is $(6a + b)(a + 6b)$ a power of two? 
Find all positive integers $a$ and $b$ for which the product $(6a + b)(a + 6b)$ is a power of $2$.

I havnt been able to get this one yet, found it online, not homework!
any help is appreciated thanks!

Assume, (6a + b)(a + 6b) = 2^c
where, c is an integer ge 0
Assume, (6a + b) = 2^r
where, r is an integer ge 0
Assume, (a + 6b) = 2^s
where, s is an integer ge 0
Now, (2^r)(2^s) = 2^c
i.e. r + s = c
Now, (6a + b) + (a + 6b) = 2^r + 2^s
i.e. 7(a + b) = 2^r + 2^s
i.e. a + b = (2^r)/7 + (2^s)/7
Now, (6a + b) - ( a + 6b) = 2^r - 2^s
i.e. a - b = (2^r)/5 - (2^s)/5
Now we have,
a + b = (2^r)/7 + (2^s)/7
a - b = (2^r)/5 - (2^s)/5
Here solving for a we get, a = ((2^r)(6) - 2^s)/35
Now solving for b we get, b = ((2^s)(6) - 2^r)/35
A careful observation reveals that there are no positive integers a and b for which the product (6a + b)(a + 6b) is a power of 2.
