- #1
cragar
- 2,552
- 3
Homework Statement
Prove that if [itex] 2^{a}-1 [/itex] is prime, then [itex] n=2^{a-1}(2^{a}-1) [/itex] is perfect.
The Attempt at a Solution
So by looking at this all divisors of n will be powers of 2 times a prime to the first power or the the zero power. On the [itex] 2^{a-1} [/itex] we have (a-1)+1 choices so we have a choices for that divisor and for the prime on the right we have 2 choices. so we have 2a divisors. for the term on the left all the divisors will be [itex] 2^0+2^1+2^2 ...2^{a-1} [/itex] so should I do an induction proof to show that this sum equals some formula so that I can show all the positive divisors add up to n?