State True or False.All numbers of a Pythagorean triplet are odd.

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State True or False.

All numbers of a Pythagorean triplet are odd.

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True

False

answer is B.

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Detailed Solution

It is required to find whether all the numbers of a Pythagorean triplet are odd.
For any natural number m > 1,

(2 m) 2 + (m 2 − 1) 2 = (m 2 + 1) 2

.
So,

(2 m), (m 2 − 1), (m 2 + 1)

form a Pythagorean triplet.
Let us take m = 4, then after substitution, the numbers are 8, 15, 17.
Clearly,

82 + 152 = 172

.
Since 8 is an even number, so all numbers of a Pythagorean triplet are not odd.
Therefore, the statement is false.
Thus, option 2 is correct.

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