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由 **----** 於星期四五月 22, 2003 9:04 pm

Meowth 寫到:extract 5^m
extract 2^m
multiply the rest

you mean,
1x3x7x9 = 9(mod 10)
...
1991x1993x1997x1999=9 (mod 10)

All times up = 9 (mod 10)

There 're
4(3) + 3(16-3) + 2(80-16) + (400-80)
=12 + 39 + 128 + 320
=499 factor 5
And there are
10(1) + 9(3-1) + 8(7-3) + 7(15-7) + 6(31-15) + 5(62 - 31) + 4(125-62) + 3(250-125) + 2(500-250) + (1000-500)
=10 + 18 + 32 + 56 + 96 + 155 + 252 + 375 + 500 + 500
=1994 factor 2
So (1994-499)=1495 factor 2 remaining.

What to do next?

由 **---** 於星期四五月 22, 2003 8:47 pm

extract 5^m
extract 2^m
multiply the rest

由 **Raceleader** 於星期四五月 22, 2003 12:10 am

Mathematica - 8

由 **----** 於星期三五月 21, 2003 11:26 pm

Find the right most non-zero digit of 2000!

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[問題]Non-zero digit

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[quote="----"][quote="Meowth"]extract 5^m extract 2^m multiply the rest[/quote] you mean, 1x3x7x9 = 9(mod 10) ... 1991x1993x1997x1999=9 (mod 10) All times up = 9 (mod 10) There 're 4(3) + 3(16-3) + 2(80-16) + (400-80) =12 + 39 + 128 + 320 =499 factor 5 And there are 10(1) + 9(3-1) + 8(7-3) + 7(15-7) + 6(31-15) + 5(62 - 31) + 4(125-62) + 3(250-125) + 2(500-250) + (1000-500) =10 + 18 + 32 + 56 + 96 + 155 + 252 + 375 + 500 + 500 =1994 factor 2 So (1994-499)=1495 factor 2 remaining. What to do next?[/quote]