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Minimizing Integral Quadratic Expression (Posted on 2024-06-18)

Determine the smallest positive integer N=3a²-ab²-2b-4 for some positive integers a and b.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution?

| Comment 1 of 4

Am I missing something? If a is a positive constant, then the formula in terms of b is a downward opening parabola and so it has no minimum.

example: a=3

N=-3b^2-2b-23

has vertex when b=-1/3 so N decreases as b runs through the positive integers.

Edit: I missed something. N must also be positive, so there is a minimum. The other comments show N can equal 2 but cannot equal 1.

Edited on June 19, 2024, 8:48 am

Posted by Jer on 2024-06-18 08:47:26

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