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`m`!= 0 /\`n`!=`0`/\`n`<=`m`.We know

which implies (4).gcd( `m`,`n`)= (0) gcd( `m`-`n`,`n`)= (1) Euclid( `m`-`n`,`n`)= (definition Euclid) Euclid( `m`,`n`)`m`!= 0 /\`n`!=`0`/\`n`not <=`m`.The proof is analogous to the previous case.

Author: Wolfgang Schreiner

Last Modification: November 24, 1999