ganeshie8
  • ganeshie8
show that 12345678987654321 ≡ 0 (mod 12345679)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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UsukiDoll
  • UsukiDoll
so we're in modulo 12345679 ... and we need a zero remainder.. oh wow. x.x
UsukiDoll
  • UsukiDoll
like how many cycles of 12345679 do we have to go through to reach 12345678987654321
ganeshie8
  • ganeshie8
Yes im sure it has a pretty neat solution :)

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More answers

imqwerty
  • imqwerty
i've done this problem before :D
ParthKohli
  • ParthKohli
Facebook pages have taught me that \(111111111^2 = 12345678987654321\)
UsukiDoll
  • UsukiDoll
-_-! This is from the same book that I've used last year. I'm not sure if I made my professor solve this one lol
ganeshie8
  • ganeshie8
Haha what has that anything to do with the present problem
ParthKohli
  • ParthKohli
The missing 8 in 12345679 is mildly annoying.
UsukiDoll
  • UsukiDoll
that's number 7b. page 52 x)
UsukiDoll
  • UsukiDoll
personally , I like the previous problems on page 51 XD
ParthKohli
  • ParthKohli
\[12345679 \times 10^9 = 12345679000000000\]subtract 12345679 from this number. Woohoo.
ParthKohli
  • ParthKohli
I know that it's ugly, but what's a better way to show that something divides something other than actually finding their ratio? :P
anonymous
  • anonymous
12345678987654321=12345679987654321-1000000000 =12345679000000000+987654321-1000000000 the first term divided by 12345679 has remainder =0 And -1000000000+987654321=-12345679 divided by 12345679 remain 0 hence 12345678987654321\(\equiv\) 0 (mod 12345679)
zzr0ck3r
  • zzr0ck3r
12345678987654321=999999999*12345679
zzr0ck3r
  • zzr0ck3r
qed
ikram002p
  • ikram002p
was thinking of that the moment i saw it @zzr0ck3r :P
ganeshie8
  • ganeshie8
that factorization is pretty @ParthKohli / @OOOPS method is really clever!

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