Question

Which of the following is not a Pythagorean triple?

Answer 1

Answer:

  (7, 24, 26)

Step-by-step explanation:

A Pythagorean triple must have an odd number of even numbers. The triple (7, 24, 26) is not a Pythagorean triple.

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Additional comment

For an odd integer n, a triple can be formed as ...

  (n, (n²-1)/2, (n²+1)/2)

That is, the following will be Pythagorean triples.

• (3, 4, 5)
• (5, 12, 13)
• (7, 24, 25)
• (9, 40, 41)
• (11, 60, 61)

Another series involves even numbers and numbers separated by 2:

  (2n, n²-1, n²+1)

• (8, 15, 17)
• (12, 35, 37)
• (16, 63, 65)

In this list, if n is not a multiple of 2, the triple will be a multiple of one from the odd-number series.

It is a good idea to remember a few of these, as they tend to show up in Algebra, Geometry, and Trigonometry problems.