Modular Arithmetic Basics in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Modular Addition

What is the output of the following Python code that performs modular addition?

DSA Python

a = 17
b = 23
mod = 10
result = (a + b) % mod
print(result)

A 0

B 10

C 1

D 9

💡 Hint

Add the numbers first, then find the remainder when divided by 10.

Adding 17 + 23 gives 40. Taking 40 modulo 10 means finding the remainder when 40 is divided by 10, which is 0.

❓ Predict Output

intermediate

Modular Multiplication Result

What will be printed by this code that calculates modular multiplication?

DSA Python

x = 7
 y = 5
 mod = 12
 product = (x * y) % mod
 print(product)

A 11

B 35

C 7

D 1

💡 Hint

Multiply first, then take remainder with 12.

7 times 5 is 35. 35 modulo 12 is 11 because 12 * 2 = 24 and 35 - 24 = 11.

🧠 Conceptual

advanced

Understanding Modular Inverse

Which of the following statements correctly describes the modular inverse of a number 'a' modulo 'm'?

A A number 'x' such that (a * x) % m = 0

B A number 'x' such that (a + x) % m = 0

C A number 'x' such that (a - x) % m = 1

D A number 'x' such that (a * x) % m = 1

💡 Hint

Think about what multiplying by the inverse should do under modulo.

The modular inverse of 'a' modulo 'm' is a number 'x' that when multiplied by 'a' gives 1 modulo 'm'. This means (a * x) % m = 1.

❓ Predict Output

advanced

Output of Modular Exponentiation

What is the output of this code that calculates modular exponentiation?

DSA Python

base = 4
exponent = 13
mod = 497
result = pow(base, exponent, mod)
print(result)

A 0

B 1

C 445

D 256

💡 Hint

Use Python's built-in pow with three arguments for efficient modular exponentiation.

Using pow(4, 13, 497) computes (4^13) mod 497 efficiently, which equals 445.

🔧 Debug

expert

Identify the Error in Modular Division Code

What error will this code raise when trying to perform modular division?

DSA Python

a = 10
b = 3
mod = 7
result = (a // b) % mod
print(result)

A SyntaxError

B Wrong output due to integer division instead of modular inverse

C TypeError

D ZeroDivisionError

💡 Hint

Modular division requires multiplying by modular inverse, not integer division.

The code uses integer division (//) which does not work for modular division. It will produce a wrong output, not an error.