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Could someone please explain why 7 is being subtracted from 64 in:

$7 · 7^{k+2} + 64 · 8^{2k+1}$ to make

$7(7^{k+2} + 8^{2k+1}) + 57 · 8^{2k+1}.$

Also, how does $7^{k+2}$ get factored by 7 to make the same thing.

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up vote 4 down vote accepted

Note that $64=57+7$, so $$ 64\cdot8^{2k+1}=7\cdot8^{2k+1}+57\cdot8^{2k+1} $$

Your problem now becomes $$ 7\cdot7^{k+2}+7\cdot8^{2k+1}+57\cdot8^{2k+1}=7(7^{k+2}+8^{2k+1})+57\cdot8^{2k+1} $$

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Fixed, thanks!! – Jean-Sébastien Oct 31 '12 at 0:11
Where is the 57 coming from? That's my question. – Unknown Oct 31 '12 at 0:28
@BernieMacinflor edited for clarity – Jean-Sébastien Oct 31 '12 at 0:31
Okay, thank you. – Unknown Oct 31 '12 at 0:42

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