Algebra/NT Question

Question

Prove that a^2+b^2+c^2+d^2 = abc+abd+acd+bcd has a solution in integers for which a, b, c, d are greater than N for all real values of N.

 

Can someone help me in this question? I tried Vieta Jumping, but can't seem to get an answer.

Answer 1

Jonathan,

 

Where did you see this question? I occasionally see very hard problems such as this one posted in WyzAnt, and it really is not the best place to get help with something like this.

 

If you have access to a mathematician or college math professor near you, I recommend asking him or her. It will probably pan out better for you than waiting for an answer here (but I have been wrong about this before).