Thread: beyond modular math?

I'm looking for a different way (a shortcut if you will) to find a remainder after division. This is for extremely large numbers (ie, where n has millions of digits) where I have a lot of them to check. Let == be the mod operator. So if n==r mod p, is there a way to know what r is when n==r mod (p+1) without having to go through the entire division process? Using some small numbers for an example and doing it the long way, let n = 41284619269126841026410326501619919269146535465293 537921 and p = 297133, then n==40997 mod p. Increasing p by 1 to 297134 then gives n==142049 mod (p+1). I want to be able to find 142049 just by already knowing that n==40997 mod p. When n is extremely large I currently have to do it piecemeal with for-next loops. (I use UBASIC) When there are millions of numbers to check you can see this way will take a very long time, hence my need for a shortcut, if there is one. Does anyone know if there is a quicker way to do this? Oh and if someone could tell me how to make separate paragraphs... Enter does not seem to work. -Jay