Decide whether the two congruences 182x ? 21 mod 245 and 81x ? 141 mod 168 can be solved simultaneously, and justify your answer.
Added by Esther R.
Step 1
If they are not, then the system of congruences may not have a solution. To check if 245 and 168 are relatively prime, we can find their greatest common divisor (GCD) using the Euclidean algorithm: 245 = 1 * 168 + 77 168 = 2 * 77 + 14 77 = 5 * 14 + 7 14 = 2 Show more…
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