noperfectcuboidexists

No Perfect Cuboid Exists

See also - http://www.bearnol.pwp.blueyonder.co.uk **************************************** b^2+c^2=d^2 c^2+a^2=e^2 a^2+b^2=f^2 a^2+b^2+c^2=g^2 Smallest solution hcf[a,b,c]=1 g^2==a^2==b^2==c^2==0,1 [mod 4] => g^2==1 [mod 4] => g==1 [mod 2] g^2=a^2+d^2=b^2+e^2=c^2+f^2 one of (a,d) even, one of (b,e) even, one of (c,f) even therefore WLOG all a,b,c even => hcf[a,b,c]>=2 => contradiction, from which result follows *****************************************