Problem 20 · 2022 Math Kangaroo
Hard
Number Theory
pythagorean-triple
A circle with midpoint \((0\,|\,0)\) has a radius of 5. How many points are there on the circumference where both co-ordinates are integers?
Show answer
Answer: C — 12
Show hints
Hint 1 of 2
You need integer points with x^2 + y^2 = 25.
Still stuck? Show hint 2 →
Hint 2 of 2
List the ways 25 is a sum of two squares, then count sign and order variations.
Show solution
Approach: lattice points on the circle
- x^2 + y^2 = 25 gives (0,±5), (±5,0), (±3,±4), (±4,±3).
- That is 4 + 4 + 4 = 12 points.
Mark:
· log in to save