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Finding all prime solutions 
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#1
Feb2313, 01:42 AM

P: 1

I want to solve equation [itex]x(x+1)+y(y+1)=z(z+1)[/itex] over primes. I found a solution x=y=2, z=3 and I have a hypothesis that this is the only solution over prime numbers, but I cannot prove it or find any other solution. Any hints, please?



#2
Feb2313, 08:16 AM

Mentor
P: 11,601

I can confirm that there are no other solutions for x,y below 100 000.
The fact that 2 is in that one solution could be a hint that there are no other solutions, but I don't see a simple proof. Python:



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