Question

My proffersor gave us all to do this
It it worth 50% of my assessment score this semester but I don't really know how to even go about have been googling it online but still no luck.....

I need details analysis

Conjecture :
The equation 24b= 2(ab+1) has no
integer solutions except when b is prime
and a is odd. For b greater than 2 and
a greater than 0.,
Prove or disprove.

Answer 1

Sorry for my typo it is 2^b=2(ab+1)

Answer 2

well, ab+1 must also be a power of 2, so both a and b must be odd.
For the prime part, check Fermat's Little Theorem.