theorem.txt

Barrows remainder theorem:
==========================
( If nobody else discovered it )


Let a[1]...a[m],n  all be integers then


((a[1] mod n)(a[2] mod n)....(a[m] mon n)mod n = (a[1]*a[2]*....*a[m])mod n


Proof:

If a mod n = r 
=> a = (n*k)+r where k is an integer & r is the remainder


(n[i]+r[i])*(n[j]+r[j]) = n^2