Back to Mathematical Olympiad
Difficulty: 3/102024 IOQM 2024 (Q3)

The number obtained by taking the last two digits of 5 2024 in the same order is:

Guide / Hint

Hint 1: Start by analyzing the initial conditions and setting up the basic equations. Last two digits of 52024.

Hint 2: Look for algebraic properties, symmetry, or geometric theorems to simplify. => 52024  (mod 100).

Hint 3: Proceed with the final algebraic steps to solve the system. 54  25 (mod 100).

Solution

Step 1: Last two digits of 52024

Step 2: => 52024  (mod 100)

Step 3: 54  25 (mod 100)

Step 4: 52024  25 (mod 100)

Step 5: => last 2 digits in same order is 25

Ready to track your progress and master these topics?

Create a free account