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Almost right-angled triangles II

Problem 224

Published on Friday, 26th December 2008, 05:00 pm; Solved by 774; Difficulty rating: 75%

Let us call an integer sided triangle with sides abc barely obtuse if the sides satisfy
a2 + b2 = c2 - 1.

How many barely obtuse triangles are there with perimeter ≤ 75,000,000?