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Home » Olympiad Section » Number Theory » Number Theory Open Questions
 
Prime solutions to Diophantine equation?
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kontinuert
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#1
Prime solutions to Diophantine equation?
Hi!

I'm struggling with the following two problems:

1)
Do four different prime numbers a, b, c and d exist, such that a^3+b^3=c^3+d^3?

2)
Do four different prime numbers a, b, c and d exist, such that a^4+b^4=c^4+d^4?

Any help is appreciated!

/Kon

PostPosted: Tue Mar 04, 2008 3:12 am  Back to top 
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maxal
Riemann Hypothesis
Riemann Hypothesis


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#2
They exist:
31^3+1867^3 = 397^3 + 1861^3
and
7^4 + 239^4 = 157^4 + 227^4.

PostPosted: Tue Jun 17, 2008 9:29 am  Back to top 
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