## Almost right-angled triangles I

### Problem 223

Published on Friday, 26th December 2008, 05:00 pm; Solved by 972; Difficulty rating: 70%Let us call an integer sided triangle with sides `a` ≤ `b` ≤ `c` *barely acute* if the sides satisfy `a`^{2} + `b`^{2} = `c`^{2} + 1.

How many barely acute triangles are there with perimeter ≤ 25,000,000?