Question: If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
Options:
1
2
3
4
Correct Answer: 3
Solution:
The smallest positive integer satisfying x ≡ 3 (mod 5) is 3.
If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer
Practice Questions
Q1
If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
1
2
3
4
Questions & Step-by-Step Solutions
If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
Correct Answer: 3
Step 1: Understand what 'x ≡ 3 (mod 5)' means. It means that when you divide x by 5, the remainder is 3.
Step 2: To find the smallest positive integer x that satisfies this condition, we can start listing numbers that give a remainder of 3 when divided by 5.
Step 3: The first few positive integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We check each one to see if it gives a remainder of 3 when divided by 5.
Step 4: When we check 3, we find that 3 divided by 5 gives a remainder of 3. So, 3 is a solution.
Step 5: Since we are looking for the smallest positive integer, we can stop here because 3 is the first number we found that meets the condition.
Modular Arithmetic – Understanding congruences and how to find integers that satisfy a given modular condition.
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