Find all triplet(s) (p, q, r) of prime numbers, that satisfy this equation:
p3 = p2 + q2 + r2
Justify your answer with valid reasoning.
p^3 - p^2 is divisible by 3 for any integer >0.
The possible cases are q=r=2, or q=r=3, or one of q,r=2 with the other odd, or both of q,r=odd.
Only the second case allows a solution: (p,q,r)=(3,3,3).
**edit**
Careless and incorrect since if p=2 mod 3, p^3 - p^2 is not divisible by 3. Ignore.
Edited on May 21, 2023, 1:18 pm
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Posted by xdog
on 2023-05-21 12:22:52 |
solution
