If a ≡ 2 (mod 5) and b ≡ 3 (mod 5), what is the value of (a * b) mod 5?

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Question: If a ≡ 2 (mod 5) and b ≡ 3 (mod 5), what is the value of (a * b) mod 5?

Options:

Correct Answer: 1

Solution:

a * b ≡ 2 * 3 ≡ 6 (mod 5), which is equivalent to 1.

If a ≡ 2 (mod 5) and b ≡ 3 (mod 5), what is the value of (a * b) mod 5?

If a ≡ 2 (mod 5) and b ≡ 3 (mod 5), what is the value of (a * b) mod 5?

Step 1: Understand the notation 'a ≡ 2 (mod 5)'. This means when you divide 'a' by 5, the remainder is 2.
Step 2: Understand the notation 'b ≡ 3 (mod 5)'. This means when you divide 'b' by 5, the remainder is 3.
Step 3: Calculate the product of 'a' and 'b'. Since 'a' is congruent to 2 and 'b' is congruent to 3, we multiply these values: 2 * 3 = 6.
Step 4: Now, we need to find '6 mod 5'. This means we divide 6 by 5 and find the remainder.
Step 5: When we divide 6 by 5, the quotient is 1 and the remainder is 1 (because 6 - 5 = 1).
Step 6: Therefore, '6 mod 5' is equal to 1.
Step 7: Conclude that (a * b) mod 5 is equal to 1.

Modular Arithmetic – Understanding how to perform operations under a modulus, specifically multiplication and reduction.
Congruences – Applying the properties of congruences to simplify calculations.