Proof questions

Would this be enough to prove the assertion, as the example answer seems to take it a step further bit I don't believe that it is needed

How do you know that 8b+7 isnt a sqaure number for some value of b?

So when doing proof by contradiction you have to show that for all values of b ,8b+7 isnt a square number

A proof has to be clear reasoning where you fully justify your steps. So in the model solution, they make the odd value observation and go ahead with that to arrive at a clear contradiction, so n is not an integer. Yours is more of a proof by convenience
https://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Challen/proof/proof.html
As a bit of reflection / the idea behind the question, its clearly about square numbers and one way to handle the 8b would be to analyse the remainder of square numbers when theyre divided by 8 (so simple mod/congruence arithmetic). Its well known/easy to show that odd square numbers have a remainder of 1 when divided by 8, so the right hand side couldnt be 3, 5 or 7 (this question). But if it had been a^2 - 8b = 1, then 3,1 would be an obvious solution (by inspection).

Sure, the remainder part is more for thinking about such questions and isnt that different from the model solution. Remainder after dividing by 4 is similar. So 7 is remainder 3, 8b is remainder 0 for all b and for a odd so a=2n+1 then
(2n+1)^2 = 4n^2+4n+1
so thats remainder 1 when divided by 4, not remainder 3. So contradiction.
The only real difference with the posted proof is that theyve divided by 2 instead of 4 and pulled the odd argument from somewhere, rather than explicitly reasoning about remainders (which is taught in y4ish?).

You dont have to be a tw*t about it, my initial point was just if leaving what I did was enough. Its not, I understood the second proof I didnt need that explaining.

Ill drop out. I was explaining the idea behind the question / proof in the previous post. Simply that.

Saying its year 4 stuff is so condescending, just a bit weird