Math Problem Statement
Fin
Solution
The image shows a problem asking to "Find the whole number solutions of the congruence ." The options listed are:
- A)
- B)
- C)
- D)
Let's solve this congruence step-by-step:
Step 1: Solve the congruence
We are given the equation: Subtracting 3 from both sides: This simplifies to: which means that must be an even number.
Step 2: Check the solutions
can take values , so we need to check which of the given options contains these numbers.
Looking at the options:
- A) includes 0 but also odd numbers.
- B) contains odd numbers only.
- C) contains even numbers.
- D) includes odd and even numbers but does not start with 0.
Thus, option C is the correct answer because it contains all even numbers.
Would you like more details or have any further questions?
Related Questions:
- How do you solve linear congruences in general?
- What does the term "modulo" mean in modular arithmetic?
- How can you determine whether a congruence has a unique solution?
- What are some properties of even and odd numbers in modular arithmetic?
- Can you apply the same method to solve quadratic congruences?
Tip: When solving congruences, always try simplifying the equation step by step, and pay attention to patterns in modular systems like mod 4 or mod 5.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Modular Arithmetic
Linear Congruences
Formulas
2x + 3 ≡ 3 mod 4
x ≡ 0 mod 2
Theorems
Properties of Modular Arithmetic
Linear Congruence Theorem
Suitable Grade Level
Grades 9-12