Solve the following set of congruences:

Question

$x \equiv 2 (mod \: 17)$

$3x \equiv 4 (mod \: 19)$

$x \equiv 7 (mod \: 23)$

06 Feb 2024

Answer :

Word Count : 341

To solve this system of congruences, we can use the Chinese Remainder Theorem (CRT). Here are the steps:

1. Check if the moduli (17, 19, 23) are pairwise coprime (i.e., their greatest common divisors are all 1). In this case, they are pairwise coprime, so we can proceed.

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