first primitive Pythagorean triplets

first primitive Pythagorean triplets

(

odd cathetus

)

2

+

(

even cathetus

)

2

=

(

hypotenuse

)

2

3

2

+

4

2

=

5

2

(

←

these form the so-called

Egyptian

triangle

, known by the

pyramid

builders)

5

2

+

12

2

=

13

2

15

2

+

8

2

=

17

2

7

2

+

24

2

=

25

2

21

2

+

20

2

=

29

2

9

2

+

40

2

=

41

2

35

2

+

12

2

=

37

2

11

2

+

60

2

=

61

2

45

2

+

28

2

=

53

2

33

2

+

56

2

=

65

2

13

2

+

84

2

=

85

2

63

2

+

16

2

=

65

2

55

2

+

48

2

=

73

2

39

2

+

80

2

=

89

2

15

2

+

112

2

=

113

2

77

2

+

36

2

=

85

2

65

2

+

72

2

=

97

2

17

2

+

144

2

=

145

2

99

2

+

20

2

=

101

2

91

2

+

60

2

=

109

2

51

2

+

140

2

=

149

2

19

2

+

180

2

=

181

2

117

2

+

44

2

=

125

2

105

2

+

88

2

=

137

2

85

2

+

132

2

=

157

2

57

2

+

176

2

=

185

2

21

2

+

220

2

=

221

2

143

2

+

24

2

=

145

2

119

2

+

120

2

=

169

2

95

2

+

168

2

=

193

2

23

2

+

264

2

=

265

2

165

2

+

52

2

=

173

2

153

2

+

104

2

=

185

2

133

2

+

156

2

=

205

2

105

2

+

208

2

=

233

2

69

2

+

260

2

=

269

2

25

2

+

312

2

=

313

2

195

2

+

28

2

=

197

2

187

2

+

84

2

=

205

2

171

2

+

140

2

=

221

2

115

2

+

252

2

=

277

2

75

2

+

308

2

=

317

2

27

2

+

364

2

=

365

2

221

2

+

60

2

=

229

2

209

2

+

120

2

=

241

2

161

2

+

240

2

=

289

2

29

2

+

420

2

=

421

2

255

2

+

32

2

=

257

2

247

2

+

96

2

=

265

2

231

2

+

160

2

=

281

2

207

2

+

224

2

=

305

2

175

2

+

288

2

=

337

2

135

2

+

352

2

=

377

2

87

2

+

416

2

=

425

2

31

2

+

480

2

=

481

2

285

2

+

68

2

=

293

2

273

2

+

136

2

=

305

2

253

2

+

204

2

=

325

2

225

2

+

272

2

=

353

2

189

2

+

340

2

=

389

2

145

2

+

408

2

=

433

2

93

2

+

476

2

=

485

2

33

2

+

544

2

=

545

2

323

2

+

36

2

=

325

2

299

2

+

180

2

=

349

2

275

2

+

252

2

=

373

2

203

2

+

396

2

=

445

2

155

2

+

468

2

=

493

2

35

2

+

612

2

=

613

2

357

2

+

76

2

=

365

2

345

2

+

152

2

=

377

2

325

2

+

228

2

=

397

2

297

2

+

304

2

=

425

2

261

2

+

380

2

=

461

2

217

2

+

456

2

=

505

2

165

2

+

532

2

=

557

2

105

2

+

608

2

=

617

2

37

2

+

684

2

=

685

2

399

2

+

40

2

=

401

2

391

2

+

120

2

=

409

2

351

2

+

280

2

=

449

2

319

2

+

360

2

=

481

2

279

2

+

440

2

=

521

2

231

2

+

520

2

=

569

2

111

2

+

680

2

=

689

2

39

2

+

760

2

=

761

2

437

2

+

84

2

=

445

2

425

2

+

168

2

=

457

2

377

2

+

336

2

=

505

2

341

2

+

420

2

=

541

2

185

2

+

672

2

=

697

2

41

2

+

840

2

=

841

2

483

2

+

44

2

=

485

2

475

2

+

132

2

=

493

2

459

2

+

220

2

=

509

2

435

2

+

308

2

=

533

2

403

2

+

396

2

=

565

2

315

2

+

572

2

=

653

2

259

2

+

660

2

=

709

2

195

2

+

748

2

=

773

2

123

2

+

836

2

=

845

2

43

2

+

924

2

=

925

2

525

2

+

92

2

=

533

2

513

2

+

184

2

=

545

2

493

2

+

276

2

=

565

2

465

2

+

368

2

=

593

2

429

2

+

460

2

=

629

2

385

2

+

552

2

=

673

2

333

2

+

644

2

=

725

2

273

2

+

736

2

=

785

2

205

2

+

828

2

=

853

2

129

2

+

920

2

=

929

2

45

2

+

1012

2

=

1013

2

575

2

+

48

2

=

577

2

551

2

+

240

2

=

601

2

527

2

+

336

2

=

625

2

455

2

+

528

2

=

697

2

407

2

+

624

2

=

745

2

287

2

+

816

2

=

865

2

215

2

+

912

2

=

937

2

47

2

+

1104

2

=

1105

2

621

2

+

100

2

=

629

2

609

2

+

200

2

=

641

2

589

2

+

300

2

=

661

2

561

2

+

400

2

=

689

2

481

2

+

600

2

=

769

2

429

2

+

700

2

=

821

2

369

2

+

800

2

=

881

2

301

2

+

900

2

=

949

2

141

2

+

1100

2

=

1109

2

49

2

+

1200

2

=

1201

2

675

2

+

52

2

=

677

2

667

2

+

156

2

=

685

2

651

2

+

260

2

=

701

2

627

2

+

364

2

=

725

2

595

2

+

468

2

=

757

2

555

2

+

572

2

=

797

2

451

2

+

780

2

=

901

2

387

2

+

884

2

=

965

2

315

2

+

988

2

=

1037

2

235

2

+

1092

2

=

1117

2

147

2

+

1196

2

=

1205

2

51

2

+

1300

2

=

1301

2

725

2

+

108

2

=

733

2

713

2

+

216

2

=

745

2

665

2

+

432

2

=

793

2

629

2

+

540

2

=

829

2

533

2

+

756

2

=

925

2

473

2

+

864

2

=

985

2

329

2

+

1080

2

=

1129

2

245

2

+

1188

2

=

1213

2

53

2

+

1404

2

=

1405

2

N.B. that the lengths of the even

cathetus

and the

hypotenuse

are consecutive integers (as 1404 and 1405)
always when the corresponding

seed numbers

m

and

n

(see the parent (

http://

planetmath

.org/PythagoreanTriplet

) entry) are successive integers.

Title

first primitive Pythagorean triplets

Canonical name

FirstPrimitivePythagoreanTriplets

Date of creation

2013-10-30 13:12:58

Last modified on

2013-10-30 13:12:58

Owner

pahio (2872)

Last modified by

pahio (2872)

Numerical id

12

Author

pahio (2872)

Entry type

Example

Classification

msc 01A16

Classification

msc 11-00

Synonym

least coprime Pythagorean triplets

Related topic

PythagorasTheorem

Related topic

IncircleRadiusDeterminedByPythagoreanTriple

Related topic

ContraharmonicMeansAndPythagoreanHypotenuses

Related topic

PythagoreanHypotenusesAsContraharmonicMeans

Defines

Egyptian triangle

Generated on Thu Feb 8 19:07:05 2018 by

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