Modular Arithmetic Basics in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is modular arithmetic?

Modular arithmetic is a system of arithmetic for integers where numbers wrap around after reaching a certain value called the modulus.

beginner

What does the expression 'a % m' mean in modular arithmetic?

It means the remainder when integer 'a' is divided by the modulus 'm'. This remainder is always between 0 and m-1.

beginner

How do you add two numbers under modulus m?

Add the two numbers normally, then take the remainder when divided by m: (a + b) % m.

beginner

What is the result of (a * b) % m?

Multiply a and b normally, then take the remainder when divided by m: (a * b) % m.

intermediate

Why is modular arithmetic useful in programming?

It helps keep numbers within a fixed range, prevents overflow, and is used in hashing, cryptography, and cyclic structures.

What is the value of 17 % 5?

A 5

B 3

C 2

D 0

17 divided by 5 is 3 with remainder 2, so 17 % 5 = 2.

Which of these is true for modular addition?

A (a + b) % m = ((a % m) + (b % m)) % m

B (a + b) % m = (a + b)

C (a + b) % m = (a % b) % m

D (a + b) % m = (a % m) * (b % m)

Modular addition distributes over modulus: (a + b) % m = ((a % m) + (b % m)) % m.

What is (4 * 6) % 5?

A 2

B 4

C 3

D 1

4 * 6 = 24, 24 % 5 = 4, since 24 divided by 5 is 4 with remainder 4.

If a % m = 3 and b % m = 4, what is (a + b) % m?

A (3 + 4) % m

B 0

C Cannot determine

D 7

The sum modulo m is (3 + 4) % m. Without knowing m, we cannot simplify further.

Which of these is NOT a use of modular arithmetic?

A Cryptography

B Hashing functions

C Preventing integer overflow

D Sorting arrays

Sorting arrays does not typically use modular arithmetic.

Explain how modular addition works and why it is useful.

Think about adding two numbers and then wrapping around a fixed number.

Describe a real-life example where modular arithmetic is used.

Consider how hours reset after 12 or 24.