Euler's conjecture a^4 + b^4 + c^4 = d^4 ...

İs there its integer solution...

my friend said, (95800)^4 + (217519)^4 +(414560)^4 = (422481)^4

 

 

 

 

 

COMMENTARY: ^=EXPONENT

See Diophantine equations.

 

Now, [math] x^{4}+ y^{4}= z^{4}[/math] has no integer solutions as it is a special case of Fermat's last theorem. I not really know much about Diophantine equations in general other than it can be difficult and a large part of modern research uses tools form algebraic geometry.

 

Have you simply tried to evaluate your friend's solution?

 

I have and it works! There is at least one solution.

http://en.wikipedia.org/wiki/Euler%27s_sum_of_powers_conjecture

 

More interesting, to me, is that the identity [math]27^5 + 84^5 + 110^5 + 133^5 = 144^5[/math] was not found until nearly 200 years after Euler made his conjecture, even though the numbers involved are rather small.