MathDB

41

Part of PEN H Problems

Problems(1)

H 41

Source:

5/25/2007
Suppose that A=1,2,A=1,2, or 33. Let aa and bb be relatively prime integers such that a2+Ab2=s3a^{2}+Ab^2 =s^3 for some integer ss. Then, there are integers uu and vv such that s=u2+Av2s=u^2 +Av^2, a=u3−3Avu2a =u^3 - 3Avu^2, and b=3u2v−Av3b=3u^{2}v -Av^3.
geometry3D geometrynumber theoryrelatively primeDiophantine Equations