What is the smallest possible natural number \(n\) for which the equation \(x^2 - nx + 2014 = 0\) has integer roots?

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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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