first primitive Pythagorean triplets

${(\text{odd cathetus})}^2+{(\text{even cathetus})}^2={(\text{hypotenuse})}^2$

$3^2+4^2=5^2$ ($\leftarrow$ 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 thehypotenuse 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