Problem 3. Use the Chinese Remainder Theorem to help you find all four solutions modulo $n$ to the equation $x^2 \equiv 4 \mod 15$ (Hint: $15 = 3 \cdot 5$, try considering the congruence modulo each of these primes).
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Step 1
We have x^2 ≡ 4 (mod 3). The possible residues modulo 3 are 0, 1, and 2. Checking each residue, we find that x ≡ 1 (mod 3) and x ≡ 2 (mod 3) are the solutions to this congruence. Step 2: Consider the congruence modulo 5. We have x^2 ≡ 4 (mod 5). The possible Show more…
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