perplexus.info :: Just Math : Minimizing Integral Quadratic Expression

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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How about ...

| Comment 3 of 4 |

N=2 when (a,b) = (4,3)

If there is an analytic way to show N=1 is impossible, then this would be a full solution.

----

bestN = 100000

bestA = 0

bestB = 0

big = 2000

for a in range(1,big):

for b in range(1,big):

N = 3*a**2 - a*b**2 - 2*b - 4

if N < 1:

continue

if N < bestN:

bestN = N

bestA = a

bestB = b

print(bestN, bestA,bestB)

Posted by Larry on 2024-06-18 11:18:27

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