What is the Modulus that will satisfy the following two equations?
57,131 mod N =199 and 37,139 mod N =67. Thanks for any help.
We don't have a direct method of finding the Modulus, but we can proceed as follows:
If the Modulus =M
If the quotient =Q for the first and =q for the second, then we have:
MQ + 199 = 57,131.................(1), and:
Mq + 67 =37,139...................(2)
Will ignore the Modulus "M" for now and re-write the two equations as:
Q =57,131 - 199 =56,932.........(3)
q =37,139 - 67 =37,072.........(4). Will factor (3) and (4) as follows:
56,932 = 2^2 * 43 * 331, and:
37,072 = 2^4 * 7 * 331
From the above factorization, we can readily see that the biggest factor they have in common is =331. Then we have:
57,131 mod 331 = 199, and
37,139 mod 331 = 67. And that satisfies both equations.
