Select the correct alternative from the given choices. If a, b and c are prime numbers satisfyin

step 1 Since A, B, and C are prime numbers, we know that they're greater than one and have no positive

Select the correct alternative from the given choices. If a,...

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Key Concepts

Prime Numbers

Prime numbers are natural numbers greater than 1 that have no divisors other than 1 and themselves. In many problems, especially those in number theory, identifying primes and understanding their unique properties is essential. Their restrictive nature means that conditions involving primes often have very few solutions, which is why reasoning about primes is key in these types of problems.

Arithmetic Sequences

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. When a problem relates numbers through fixed increments, it suggests an underlying arithmetic sequence. Analyzing such sequences helps in determining whether all elements meet certain criteria, such as being prime, which is critical when conditions involve equal differences between numbers.

Systems of Equations

A system of equations involves multiple equations that specify relationships among the same set of variables. Solving these systems requires finding values that satisfy all equations simultaneously. This concept is important because it provides a framework for understanding how different constraints interact, especially when those constraints reduce the problem to checking a limited set of possibilities.

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