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Undergrad Finding smallest solution to modular equations
Well, aside from 4, the each congruence will have at most (p+1)/2 values for a prime p. So the number of possibilities will roughly be the product of the first N primes (aside from 2, for which 4 is used instead) divided by 2^N. For many congruences, this gives way too many possibilities to...- Das Bot
- Post #8
- Forum: Linear and Abstract Algebra
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Undergrad Finding smallest solution to modular equations
The chinese remainder theorem will give a solution, but I don't know if the smallest solution will be either 1 or 2 mod 3.- Das Bot
- Post #6
- Forum: Linear and Abstract Algebra
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Undergrad Finding smallest solution to modular equations
Thank you for the replies :) Simply adding 4 will surely give an answer, but when at some point I am dealing with houndreds of congruences and an answer in the range [10^20, 10^25] this is proving too slow. My present algorithm for finding a solution is to line up the equations, and if some...- Das Bot
- Post #4
- Forum: Linear and Abstract Algebra
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Undergrad Finding smallest solution to modular equations
Hallo I have gotten the task of finding the smallest number which is: 1 or 2 mod 3 0 mod 4 0 or 1 or 4 mod 5 1, 2, 5, 6, 9 or 10 mod 11 I have also been given that the smallest number is in the range [10,50]. Now, it is quite easy...- Das Bot
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- Replies: 7
- Forum: Linear and Abstract Algebra