Diophantine Equation—5th Powers

Author

Eric W. Weisstein
May 2, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DiophantineEquations/DiophantineEquation5thPowers.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/DiophantineEquation5thPowers.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Check

Equal@@@Map[Plus@@#&,Map[HoldForm[#^5]&,LikePowers[5,1,4],{3}],{2}]//ColumnForm

Equal@@@Map[Plus@@#&,LikePowers[5,1,4]^5,{2}]

Piezas k.4.4

eqn=With[{u=a^2-b^2,v=b^2-c^2},((-a+b+c)x^2+2(c u-b v)x y-(a+b+c)u v y^2)^k+((a-b+c)x^2+2(c u+b v)x y+(a+b-c)u v y^2)^k+((a+b-c)x^2+2(-c u-b v)x y+(a-b+c)u v y^2)^k+(-(a+b+c)x^2+2(-c u+b v)x y+(-a+b+c)u v y^2)^k-(-(a+b+c)x^2+2(-b u+a v)x y+(a+b-c)u v y^2)^k-((a+b-c)x^2+2(b u-a v)x y-(a+b+c)u v y^2)^k-((a-b+c)x^2+2(-b u-a v)x y+(-a+b+c)u v y^2)^k-((-a+b+c)x^2+2(b u+a v)x y+(a-b+c)u v y^2)^k];

Expand[eqn/.k->1]

(Expand[eqn/.k->#]===0)&/@Range[5]