[seqfan] Re: Number theory question

[M. F. Hasler]

On Wed, May 31, 2017 at 4:12 AM, David Wilson <davidwwilson at comcast.net>
wrote:

> Let !n = 0! + 1! + ... + n! = A003422(n)
> For integer k, is it true that
>         !a == k (mod a)
> and
>         !b == k (mod b)
> together imply
>         !c == k (mod c)
> where
>         c = lcm(a, b)
> ?
>

Yes: since x! == 0 (mod y) for all x >= y,
you have for c >= a, c >= b:
!c == !a (mod a)  and  !c == !b (mod b).
Also, in general,
!c == k (mod a) and  !c == k (mod b) implies !c == k (mod LCM(a,b)).

- Maximilian