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The discriminant of the above equation should be a perfect square for the equation to have integral roots. So the smallest value of n for which it is a perfect square is 91.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestLet the roots of the equation be $\alpha$ and $\beta$.

Then $n = \alpha + \beta$ and $2014 = \alpha \beta$.

The possible integral pairs of $(\alpha, \beta)$ are $(1, 2014), (2, 1007), (19, 106),$ and $(38, 53)$.

Therefore, the possible values of $n$ are $2015, 1009, 125$ and $91$. The minimum value is $91$, so $n = \boxed{91}$

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Is the answer 91?

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Yes , it is 91 :D

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Yayy!! lol:D:D

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Explain?

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The discriminant of the above equation should be a perfect square for the equation to have integral roots. So the smallest value of n for which it is a perfect square is 91.

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91

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91

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91

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