A Pythagorean Triplet has 3 numbers a, b, c

and

**
a
**
^{
2
}
**
+ b
**
^{
2
}
**
= c
**
^{
2
}

Thus, we say that (a, b, c) are Pythagorean triplet

__
Note
__

**:**This a, b, c are sides of a right triangle

The most common Pythagorean Triplets are

- 3, 4, 5
- 5, 12, 13
- 7, 24, 25
- 8, 15, 17

Let’s see how we check them

####
**
For Numbers 3, 4, 5
**

3
^{
2
}
+ 4
^{
2
}
= 9 + 16

= 25

= 5
^{
2
}

∴ 3
^{
2
}
+ 4
^{
2
}
= 5
^{
2
}

Thus, 3, 4, 5 are Pythagoras Triplets.

####
**
For Number 5, 12, 13
**

5
^{
2
}
+ 12
^{
2
}
= 25 + 144

= 169

= 13
^{
2
}

Thus, 5, 12, 13 are Pythagorean Triplets.

**
For Numbers
**
**
7
**
**
, 24, 25
**

3
^{
2
}
+ 4
^{
2
}
= 9 + 16

= 25

= 5
^{
2
}

∴ 3
^{
2
}
+ 4
^{
2
}
= 5
^{
2
}

Thus, 3, 4, 5 are Pythagoras Triplets.

**
For Number 5, 12, 13
**

5
^{
2
}
+ 12
^{
2
}
= 25 + 144

= 169

= 13
^{
2
}

Thus, 5, 12, 13 are Pythagorean Triplets.

**
In General
**

**
(2m)
^{
2
}
+ (m
^{
2
}
- 1)
^{
2
}
= (m
^{
2
}
+ 1)
^{
2
}
**

Here,

First number = 2m

Second number = 2m

Third number = m
^{
2
}
+ 1

from Pythagoras Triplets.

**
Note:
**

If we know that 3, 4, 5 are Pythagorean Triplets

Then,

3 × 2 = 6

4 × 2 = 8

5 × 2 = 10

So, (6, 8, 10) will also be a Pythagorean Triplet

Similarly, if we multiply by 3

(9, 12, 15) is also a Pythagorean Triplet

And, more generally, if we multiply by any number k

(3k, 4k, 5k) will also be a Pythagorean Triplet