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4 cards from this section. Quick, good the night before a test.
What is the solution for the linear congruence 4x ≡ 2 (mod 6)?
Use the concept of divisibility in modular arithmetic.
How do you express solutions for 3x ≡ 1 (mod 8)?
Find an integer such that `3 * ? ≡ 1 (mod 8)`.
What is the general solution format for 6x ≡ 4 (mod 10)?
Think about how the solution can be expressed with `k` integer.
True or False: The Extended Euclidean Algorithm can be applied if gcd(a, N) is greater than 1.
Recall the conditions for the applicability of this algorithm.
Solve the following system using the Chinese Remainder Theorem: x ≡ 4 (mod 5), x ≡ 1 (mod 3), x ≡ 2 (mod 7). Provide full steps in your reasoning.
Start by calculating the product of moduli.
Employ the Extended Euclidean Algorithm to find the multiplicative inverse of 7 mod 26. Show your steps.
Remember the last non-zero remainder should give you the gcd proof.
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