(* Check for the theorem of Elkahhar These parameters r and q will create a,b,c and k,l,m as stated in the theorem page *) (*--------------------------------*) r=27 ; q=3 ; (* With the condition r<>q *) (*--------------------------------*) Q:=2*(r^2+q^2)-1 Z:=(Q^2+32*r^2*q^2)*(r^2+q^2) a:=Z-3*r^2*Q^2 b:=Z-96*r^2*q^4 c:=Z-3*q^2*(Q^2+32*r^4) k:=Z-3*q^2*Q^2 l:=Z-96*r^4*q^2 m:=Z-3*r^2*(Q^2+32*q^4) seventh:=(a^7+b^7+c^7)/(k^7+l^7+m^7) fifth:=(a^5+b^5+c^5)/(k^5+l^5+m^5) third:=(a^3+b^3+c^3)/(k^3+l^3+m^3) prod:=(a*b*c)/(k*l*m) Print["------------------------"] Print["a= ",a] Print["b= ",b] Print["c= ",c] Print["--------------"] Print["k= ",k] Print["l= ",l] Print["m= ",m] Print["------------------------"] TrueQ[seventh==fifth] TrueQ[seventh==third] TrueQ[seventh==prod] Print["------------------------"] TrueQ[a+b+c==0] TrueQ[k+l+m==0] TrueQ[a^2+b^2+c^2==k^2+l^2+m^2] TrueQ[a^4+b^4+c^4==k^4+l^4+m^4] Print["------------------------"] ------------------------ a= -2997536049 b= 1754887122 c= 1242648927 -------------- k= 1701813951 l= 1301390802 m= -3003204753 ------------------------ True True True ------------------------ True True True True ------------------------