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Math question anti-mod?

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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.

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