## ganeshie8 one year ago show that 12345678987654321 ≡ 0 (mod 12345679)

1. UsukiDoll

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

2. UsukiDoll

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

3. ganeshie8

Yes im sure it has a pretty neat solution :)

4. imqwerty

i've done this problem before :D

5. ParthKohli

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

6. 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

7. ganeshie8

Haha what has that anything to do with the present problem

8. ParthKohli

The missing 8 in 12345679 is mildly annoying.

9. UsukiDoll

that's number 7b. page 52 x)

10. UsukiDoll

personally , I like the previous problems on page 51 XD

11. ParthKohli

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

12. 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

13. 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)

14. zzr0ck3r

12345678987654321=999999999*12345679

15. zzr0ck3r

qed

16. ikram002p

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

17. ganeshie8

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