Prove all even perfect numbers will end in 6 or 8.

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- Apr 16th 2007, 01:55 PMfifthrapiersEven Number Proof
Prove all even perfect numbers will end in 6 or 8.

- Apr 16th 2007, 05:24 PMThePerfectHacker
Since it is even we can write, by Euler,

n=2^{k-1}*(2^k-1) ---> Note k must be a prime.

Trivial for k=2. Assume k>2.

Divide the proof into two cases.

**Case I**If k=4j+1 then just by working modulo 10 you find that n = 6 (mod 10).

**Case II**If k=4j+3 then just be working modulo 10

you find that n = 8 (mod 10).