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Math Help - Even Number Proof

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    Even Number Proof

    Prove all even perfect numbers will end in 6 or 8.
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  2. #2
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    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).
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