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looking for integer pairs (a,b) $(a,c)$ such that $4a^2 + 8c^2 - 4c + 1$ is a perfect squareHi. I'm looking to find integer pairs $(a,b)$ (a,c)$ such that $4a^2 + 8c^2 - 4c +1$ is a perfect square. The sum is odd so I set the sum equal to $(2n+1)^2$ to cancel out the 1s and I end up with $\boxed{a^2 + 2c^2 - c = n^2 + n}$. I haven't found a valid technique to break this down yet but I think it could be a pell's equation in disguise. I'm wondering if anyone can give me some insight on this problem. Thanks. |
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looking for integer pairs (a,b) such that $4a^2 + 8c^2 - 4c + 1$ is a perfect squareHi. I'm looking to find integer pairs $(a,b)$ such that $4a^2 + 8c^2 - 4c +1$ is a perfect square. The sum is odd so I set the sum equal to $(2n+1)^2$ to cancel out the 1s and I end up with $\boxed{a^2 + 2c^2 - c = n^2 + n}$. I haven't found a valid technique to break this down yet but I think it could be a pell's equation in disguise. I'm wondering if anyone can give me some insight on this problem. Thanks.
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