Implement Shamir's Secret Sharing reconstruction
bash, 271 chars

r(){
[ ${1/0/} ]&&{ r $(($2%$1)) $1;((t=u,u=v-$2/$1*u,v=t));}
}
read
((N=1928049029,n=0))
while read x[$n] y[$n]
do((n++))
done
for((i=n;z=(z+l)%N,i--;))do
for((j=n,l=y[i];j--;))do
((u=0,v=1,d=x[j]-x[i],M=N+d))
r M N
[ ${d/0/} ]&&((l=l*x[j]%N*(u+N)%N))
done
done
echo $z

The newlines could be replaced in most cases with semicolons, but I don't think there's any unnecessary whitespace.

(I hadn't realised before today that bash's integers are 64-bit - very helpful).

For bash the recursive GCD (exploiting global state) seems to be more compactible than the iterative one. This is mostly straightforward; the interesting trick is [ ${d/0/} ]&amp;&amp;foo which is effectively if [ $d -ne 0 ];then foo;fi