HP 15C: Pythagorean
Triples
This program calculates the Pythagorean triple (A, B, C)
such that A^2 + B^2 = C^2 by the formulas:
A = K * (M^2 – N^2)
B = K * (2 * M * N)
C = K * (M^2 + N^2)
The conditions are M, N, and K are all positive integers
where M > N.
Store M into memory 0, N into memory 1, and K into memory
2. A, B, and C are stored in memories 3,
4, and 5, respectively. If no such
combination can be found, a single zero (0) is returned.
Step

Key

Code

001

LBL A

42, 21, 11

002

RCL 1

45, 1

003

RCL 0

45, 0

004

X≤0

43, 10

005

GTO 0

22, 0

006

RCL 0

45, 0

007

X^2

43, 11

008

RCL 1

45, 1

009

X^2

43, 11

010



30

011

STO 3

44, 3

012

LST X

43, 36

013

2

2

014

*

20

015

+

40

016

STO 5

44, 5

017

RCL 0

45, 0

018

RCL* 1

45, 20, 1

019

2

2

020

*

20

021

STO 4

44, 4

022

RCL 2

45, 2

023

STO* 3

44, 20, 3

024

STO* 4

44, 20, 4

025

STO* 5

44, 20, 5

026

RCL 3

45, 3

027

X^2

43, 11

028

RCL 4

45, 4

029

X^2

43, 11

030

+

40

031

RCL 5

45, 5

032

X^2

43, 11

033



30

034

X=0

43, 20

035

GTO 1

22, 1

036

LBL 0

42, 22, 1

037

0

0

038

RTN

43, 32

039

LBL 1

42, 21, 1

040

RCL 3

45, 3

041

R/S

31

042

RCL 4

45, 4

043

R/S

31

044

RCL 5

45, 5

045

RTN

43, 32

Example: Input: R0 = M = 4,
R1 = N = 1, R2 = 2. Output: 30, 16, 34
This blog is property of Edward Shore, 2017.