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Found problems: 1

2008 Costa Rica - Final Round, 5
Let $ p$ be a prime number such that $ p\minus{}1$ is a perfect square. Prove that the equation $ a^{2}\plus{}(p\minus{}1)b^{2}\equal{}pc^{2}$ has infinite many integer solutions $ a$, $ b$ and $ c$ with $ (a,b,c)\equal{}1$
diophantine equation other problems Diophantine equations algebra number theory