Hello,

On Thu, Feb 18, 2010 at 1:07 AM, Harald Schilly
<harald.schi...@gmail.com> wrote:
> On Feb 18, 2:21 am, Oscar Gerardo Lazo Arjona
> <algebraicame...@gmail.com> wrote:
>> I have the feeling that this is a
>> more profound problem than it appears (finding integer solutions).
>>
>
> ... and I have the feeling that you can do this rather directly with
> Sage's CRT_list function, but I'm unable to solve it.

You only need to include the number of columns which are coprime:

sage: CRT_list([2,3,4,0],[3,4,5,7])
119
sage: [119%i for i in range(2,8)]
[1, 2, 3, 4, 5, 0]
sage: lcm([3,4,5,7])
420
sage: [(119+420*3)%i for i in range(2,8)]
[1, 2, 3, 4, 5, 0]

Any positive integer which is conguent to 119 mod 420 will work.

--Mike

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