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Find remainder
04-16-2010, 01:15 PM
Post: #1
Find remainder
Find the remainder when \(9\times 99\times 999\times\cdots\times\underbrace{99\cdots9}_{\text{999 9's}} \) is divided by \(1000\)
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04-21-2010, 05:03 PM
Post: #2
RE: Find remainder
\(9\times99(10^3-1)(10^4-1)\cdots(10^999 -1) = 891(10^3M+(-1)^{999-3+1})=891(1000M-1)\)
\( \equiv 1000-891\pmod {1000 } \equiv 109 \pmod{1000}\)
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