Question: In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
Options:
a - b is divisible by m
a + b is divisible by m
a * b is divisible by m
a / b is divisible by m
Correct Answer: a - b is divisible by m
Solution:
The statement a ≡ b (mod m) means that the difference a - b is divisible by m.
In a modular arithmetic system, if a ≡ b (mod m), which of the following stateme
Practice Questions
Q1
In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
a - b is divisible by m
a + b is divisible by m
a * b is divisible by m
a / b is divisible by m
Questions & Step-by-Step Solutions
In a modular arithmetic system, if a ≡ b (mod m), which of the following statements is true?
Step 1: Understand what 'a ≡ b (mod m)' means. It means that when you divide a and b by m, they leave the same remainder.
Step 2: Recognize that if a and b leave the same remainder when divided by m, then the difference (a - b) must be a multiple of m.
Step 3: Conclude that 'a - b' is divisible by m, which is the key idea behind modular arithmetic.
Modular Arithmetic – Modular arithmetic involves integers and a modulus, where two numbers are considered equivalent if their difference is divisible by the modulus.
Divisibility – Understanding that if a ≡ b (mod m), then a - b is a multiple of m, which is a key property of modular arithmetic.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
