show that
12345678987654321 ≡ 0 (mod 12345679)

Question

show that
12345678987654321 ≡ 0 (mod 12345679)

usukidoll · Answer

so we're in modulo 12345679 ... and we need a zero remainder.. oh wow. x.x

usukidoll · Answer

like how many cycles of 12345679  do we have to go through to reach 12345678987654321

ganeshie8 · Answer

Yes im sure it has a pretty neat solution :)

imqwerty · Answer

i've done this problem before :D

parthkohli · Answer

Facebook pages have taught me that $111111111^2 = 12345678987654321$

usukidoll · Answer

-_-! 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 · Answer

Haha what has that anything to do with the present problem

parthkohli · Answer

The missing 8 in 12345679 is mildly annoying.

usukidoll · Answer

that's number 7b. page 52 x)

usukidoll · Answer

personally , I like the previous problems on page 51 XD

parthkohli · Answer

$$12345679 \times 10^9 = 12345679000000000$$subtract 12345679 from this number. Woohoo.

parthkohli · Answer

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 · Answer

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 · Answer

12345678987654321=999999999*12345679

zzr0ck3r · Answer

qed

ikram002p · Answer

was thinking of that the moment i saw it @zzr0ck3r  :P

ganeshie8 · Answer

that factorization is pretty
@ParthKohli  / @OOOPS method is really clever!