## Finding all prime solutions

I want to solve equation $x(x+1)+y(y+1)=z(z+1)$ 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?
 PhysOrg.com science news on PhysOrg.com >> A robot that runs like a cat (w/ Video)>> Global cooling as significant as global warming, research shows>> 'Chase and run' cell movement mechanism explains process of metastasis
 Mentor 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: Code: def isprime(n): for x in range(2, int(n**0.5)+1): if n % x == 0: return False return True primes= [] for x in range(2,100000): if(isprime(x)): primes.append(x) for x in primes: if(x%1000==1): print("computing: ",x) for y in primes: zz=x*(x+1)+y*(y+1) z=1/2*(1+4*zz)**0.5-1/2 if(round(z,0)==z and isprime(z)): print(x,y,round(z,0))
 Recognitions: Gold Member The terms A(A+1) are twice the sum of a series, dividing by 2 we get an equation that says: I need to sums of series that add to a third sum. This is about as far as I got, May not be much help but is a different view.

 Similar Threads for: Finding all prime solutions Thread Forum Replies Calculus & Beyond Homework 1 Linear & Abstract Algebra 20 Calculus & Beyond Homework 3 General Math 2 Introductory Physics Homework 2