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More Triangle Numbers (Posted on 2004-01-15) Difficulty: 2 of 5
Triangle numbers are calculated taking each integer plus all the ones before it. The first triangle number is 1, the second is 1+2 or 3, and the third is 1+2+3 or 6.

If you take 8 times a triangle number plus 1, the result will be a perfect square. This number also will be the square of the triangle number's place doubled, plus one.

For example, 6 is third in the triangle number sequence. (1, 3, 6...) This means 8 times 6 plus 1 = 49 equals 3 times 2 plus 1, squared, or 7 squared.

Prove why this works.

See The Solution Submitted by Gamer    
Rating: 3.0000 (4 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-11-14 06:03:19
No SubjectSRay2005-03-22 16:13:38
SolutionGeometric Solutionnikki2005-01-27 21:23:40
SolutionLarry2004-01-28 20:18:12
Solutionarithmaticelybharath2004-01-15 13:29:10
SolutionGeometricallye.g.2004-01-15 10:13:08
SolutionSolutionPenny2004-01-15 09:34:21
Solutionretiarius2004-01-15 09:04:28
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