The only two divisors of a prime is 1 and itself and so, the sum of its divisors is p + 1:
Now apply this to both sides:
a) Let p and p+2 be twin primes. Prove that sigma(P+2)=sigma(p) + 2
b)Prove or disprove the converse of part a above.
For Part a i just can seem to equate the 2.
I get that sigma(P+2) is [(P+2)^2 - 1]/[(P+2)-1] and rearranging i get
P^2 + 4p +4 / P+1
and then i get that sigma(P) +2 is [P^2-1/P-1] + 2 and rearranging i get
2p^2 +4p -6 / 2(P-1)
Maybe i am approaching it the wrong way?