I have downloaded an algorithm from Rosetta Stone website that uses Modular inverse to compute Chinese remainder theorem (CRT). In other words it will need to use the extended euclidean algorithm and this requires GCD to be 1. If GCD is not 1 then there is no inverse and so the CRT algorithm returns the word "fail" when you have GCD greater than 1.
I also know that there are other questions asked on this website that attempt to deal with this matter. There are 3 Qs actually posted. The leading Q is at Chinese Remainder Theorem When GCD is not 1.
But I could not fathom how to solve my question from that post so I am asking for a simpler and more direct answer and to this end I will state an example question as follows:
The divisors are 91 and 35 respectively. Note that the GCD between them is 7.
From the first divisor is a remainder of 43 and from the second divisor is a remainder of 29. So now how do you find the single CRT value that when divided separately by each divisor of 91 and 35 respectively will yield each of the remainders 43 and 29 respectively?
Wherever you want to point out a simpler answer do so. If that is in a previous question point it out to me or try to answer the matter in this question post. do help.
