The smallest integer that produces remainders of $2$, $4$,$ 6$ and $1$ when divided by$ 3$, $5$,$ 7$ and $11$ respectively is?

Question

I am finding the Chinese Remainder theorem very complicated, Any other wa to solve this will be really helpful,

Thanks in advance!

As asked there is no answer. You can subtract $1155$ from any solution and get another. There are infinitely large negative solutions, so if you consider $-1156$ smaller than $-1$ you can always find a smaller integer. — Ross Millikan, May 07 '17 at 00:01

score 2 · Answer 1 · answered May 06 '17 at 23:35

2

Note that $-1$ solves the $3,5,7$ cases, so $-1 \pmod {105}$ will work for those. Now you just have two moduli to worry about.

answered May 06 '17 at 23:35

Ross Millikan

How can i solve the last two equations without using mod? – onelessproblem May 06 '17 at 23:41
You need to use mod, but this has made it much easier. You can just look through $-1, 104, 209, \ldots$ for one that is $1 \pmod {11}$ – Ross Millikan May 06 '17 at 23:59

1 Answers1