I am currently studying discrete mathematics at uni (in my computer science degree). We have an assignment due tomorrow, and i have been able to do most of it, but one question eludes me. I spoke to a tutor today about it, and he said that last year they asked the same question in the assignment, and only 4 people got it right in the entire course.
The question is this: given the possible remainders that a perfect square leaves when divided by $3, 4$ and $8$......., $a, b$ are in the natural numbers, find all solutions to $2^a = b^2 - 5$ and prove there are no more solutions than the ones you have found?
I have been trying all day to solve this, but i am still no closer.
I am guessing it has something to do with using a different modulus (one of the tutors hinted this), but i cant figure it out.
If someone wouldn't mind perhaps pointing me in the right direction, i would be hugely grateful.
Thanks Corey B :)