Hint 1: A longer list:
- 1 = 1² + 0²
- 2 = 1² + 1²
- 3 (No)
- 4 = 2² + 0²
- 5 = 2² + 1²
- 6 (No)
- 7 (No)
- 8 = 2² + 2²
- 9 = 3² + 0²
- 10 = 3² + 1²
- 11 (No)
- 12 (No)
- 13 = 3² + 2²
- 14 (No)
- 15 (No)
- 16 = 4² + 0²
- 17 = 4² + 1²
- 18 = 3² + 3²
- 19 (No)
- 20 = 4² + 2²
- 21 (No)
- 22 (No)
- 23 (No)
- 24 (No)
- 25 = 5² + 0² = 4² + 3²
- 26 = 5² + 1²
- 27 (No)
- 28 (No)
- 29 = 5² + 2²
- 30 (No)
Hint 2: Consider the numbers that leave a remainder of 3 when you divide by 4.
Hint 3: If two numbers both work, then what about their product?
