If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
Practice Questions
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If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
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The smallest positive integer satisfying x ≡ 3 (mod 5) is 3.
Questions & Step-by-step Solutions
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Q
Q: If x ≡ 3 (mod 5), what is the value of x when x is the smallest positive integer?
Solution: The smallest positive integer satisfying x ≡ 3 (mod 5) is 3.
Steps: 5
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.
