IMC 2016 Q3
3. How many of these five expressions give answers which are not prime numbers?
\(1^2 + 2^2\) \(2^2 + 3^2\) \(3^2 + 4^2\) \(4^2 + 5^2\) \(5^2 + 6^2\)
- A 0
- B 1
- C 2
- D 3
- E 4
Intermediate Mathematical Challenge 2016, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 1
The values of the five expressions are 5, 13, 25, 41 and 61 respectively. Of these, only 25 is non-prime.
Solution © UK Mathematics Trust, from the IMC 2016 solutions. Longer versions with investigations: Solutions and investigations (PDF).