Math Problem Statement

To solve the system of congruences:

20x≡24mod  16420x≡24mod164

x≡15mod  73x≡15mod73

Solution

To solve the given system of congruences:

20x &\equiv 24 \pmod{164}, \\ x &\equiv 15 \pmod{73}, \end{aligned}$$ we'll use the following steps: ### Step 1: Solve the first congruence $$20x \equiv 24 \pmod{164}$$ - First, simplify the congruence by dividing both sides by the greatest common divisor (GCD) of 20 and 164. The GCD of 20 and 164

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Math Problem Analysis

Mathematical Concepts

Modular arithmetic

Formulas

Chinese Remainder Theorem

Theorems

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Suitable Grade Level

Advanced High School and Above

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