Question 65

State whether the following statement is true or false:

For every natural number $m$ , $(2 m - 1, 2 m^{2} - 2 m$ , $2 m^{2} - 2 m + 1$ ) is a pythagorean triplet.

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Solution

False
$∵$ $(2 m - 1)^{2} \neq (2 m^{2} - 2 m)^{2} + (2 m^{2} - 2 m + 1)^{2}$
$(2 m^{2} - 2 m)^{2} \neq (2 m - 1)^{2} + (2 m^{2} - 2 m + 1)^{2}$
and $(2 m^{2} - 2 m + 1)^{2} \neq (2 m - 1)^{2} + (2 m^{2} - 2 m)^{2}$

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