Math question anti-mod?

[Endy]

Is it possible to determine the anti-mod of a number. That is from a remainder and a number, determine the other number?

I can't quite put it in words but I feel like it'd be very useful. It probably exists already I'm just not finding much about it.

[Numsgil]

The problem of course is that the anti mod wouldn't be a single number, it would be a whole set of numbers.  This is called an equivelance class or equivelance relation or something like that.

So the "antimod" of 3 in mod 7 would be: {3, 10, 17,  etc.}

[Endy]

What if you used zero as the remainder and a factor of primes as the number? Theorectically you could obtain the two prime numbers with it.

[Numsgil]

I'm not sure I understand what you mean.

[Endy]

Zero is the remainder whenever there is a perfect division. A product of primes only has two such divisors the two primes. If mod could be reversed the primes could be found.

Thereby solving multiple challenges and winning tons of money.

A/B=C remainder=0

Therefore:

0 antimod A = [B,C]

Probably hopeless, still should never stop trying.

[Ulciscor]

A product of primes is divisible by one, which isn't a prime number. Am I missing something here?

[Numsgil]

It could be a multiple of the product of the two primes.  For instance, if your two primes are 2 and 3, and you have 30 as the number, then you end up with a mod of 0.

However, a 5 has managed to creep into your number, which messes things up.

Modular math theory is covered in a subject called Abstact Algebra.  If you're interested, you should try and find a book on it at a library somewhere.

[Endy]

Okay, thanks