Question

Verify p divides a^2 if p=2,a=(1,2,3,4,5)

Answer 1

Answer:

Step-by-step explanation:

This is what I got so far. I figured that since p,q are bigger than 5, there are only odd primes for this conjecture. Then I can rename p=2m+1,q=2n+1,m,n∈Z. We want to show (p2−q2)=24k,k∈Z. By substituting 2m+1 for p and 2n+1 for q, we get ((2m+1)2−(2n+1)2). If we expand it, we get 4(m2+n2+m−n) Q. I think I can make 4(m2+n2+m−n) look like 24k. How should I approach

And my prof. commented that "I would take this proof in small steps. Rather than trying initially to prove that 24|p2−q2, look at the progress you already have. You proved 4|p2−q2. Can you prove 8 is a factor? What about 3? Then see if you can put together what you have to get 24 as a factor."