How many three odd consecutive integers are there between 1 and 2000 whose sum is a perfect square? Thank you.

Guest Sep 25, 2022

#1**0 **

Here's a hint: The 3 numbers can only sum to a square if the square is divisible by 3

BuilderBoi Sep 25, 2022

#2**0 **

1 = (1, 3, 5) = 9

2 = (25, 27, 29) = 81

3 = (73, 75, 77) = 225

4 = (145, 147, 149) = 441

5 = (241, 243, 245) = 729

6 = (361, 363, 365) = 1089

7 = (505, 507, 509) = 1521

8 = (673, 675, 677) = 2025

9 = (865, 867, 869) = 2601

10 = (1081, 1083, 1085) = 3249

11 = (1321, 1323, 1325) = 3969

12 = (1585, 1587, 1589) = 4761

13 = (1873, 1875, 1877) = 5625

Guest Sep 25, 2022