IKMC 2025 - Grades 11-12 - Set 2 - Self-study Question 21

Question 21

A student starts with the two numbers 3 and 5. Each operation replaces the two numbers by their sum and their positive difference. After 50 operations, what two numbers remain?

Question illustration

$3^{25}$ and $5^{25}$
$3^{50}$ and $5^{50}$
$2\cdot3^{25}$ and $2\cdot5^{25}$
$3\cdot2^{25}$ and $5\cdot2^{25}$
None of the previous choices