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By function definition, we have four cases:

`m`= 0.By (3), we have

`n`!= 0 and, by definition of gcd and Euclid,gcd(

which implies (4).`m`,`n`) =`n`= Euclid(`m`,`n`)`m`!= 0 /\`n`=`0`.We have, by definition of gcd and Euclid,

gcd(

which implies (4).`m`,`n`) =`m`= Euclid(`m`,`n`)

Author: Wolfgang Schreiner

Last Modification: November 24, 1999