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Chinese remainder theorem, urgent!
This is an attempt to make the Chinese Remainder Theorem more concrete.
Let m = 206 and n = 125. You may use the fact that 89n - 54m = 1.
(a) What does the Chinese Remainder Theorem have to say about pairs
of residues modulo 206 and 125? How do you know that it applies?
(b) Find residues x and y modulo mn = 25,750 where
x = 1 (mod m); x = 0 (mod n);
y = 0 (mod m); y = 1 (mod n):
(c) Find a residue z modulo 25,750 where
z = 10 (mod m); z = 24 (mod n):
see above
for part a) CRT says that there is a unique N modulo mn such that N=a mod m and N=b mod n. I don't know what "How do you know that it applies means". The problem set is due in a couple of hours. I would be very grateful for any help.
Homework Statement
This is an attempt to make the Chinese Remainder Theorem more concrete.
Let m = 206 and n = 125. You may use the fact that 89n - 54m = 1.
(a) What does the Chinese Remainder Theorem have to say about pairs
of residues modulo 206 and 125? How do you know that it applies?
(b) Find residues x and y modulo mn = 25,750 where
x = 1 (mod m); x = 0 (mod n);
y = 0 (mod m); y = 1 (mod n):
(c) Find a residue z modulo 25,750 where
z = 10 (mod m); z = 24 (mod n):
Homework Equations
see above
The Attempt at a Solution
for part a) CRT says that there is a unique N modulo mn such that N=a mod m and N=b mod n. I don't know what "How do you know that it applies means". The problem set is due in a couple of hours. I would be very grateful for any help.