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Question

Prove the equality:
(666...6)2+888....8=444...4
n digits n digits 2n digits

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Solution

Represent each number as a G.P e.g., we write 6666 as
6+6.10+6.102+++6.10n1
=6(10n1)101=23(10n1) etc.
Hence we have to prove that
[23(10n1)]2+89(10n1)=49(102n1)
Now cancel 19(10n1)
4(10n1)+8=419(10n+1)
Above is clearly true.

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