Wikipedia:Reference desk/Archives/Mathematics/2021 August 26

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August 26

minimum composite Quadratic...

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This is sort of shower though that I'm having problems working out. Let A, B & C be composite positive integers without a single common factor for all three (so 10, 12 & 15 would be allowed). Let the quadratic equation Ax^2+Bx+C be factorable into (px+q)(rx+s) where p,q,r &s are integers. Let Z=A+B+C. What is the minimum possible value for Z?Naraht (talk) 13:16, 26 August 2021 (UTC)

I suspect it's 25 from $4x^{2}+12x+9=(2x+3)^{2}$--2406:E003:849:5501:E1BB:865D:D6E6:9D8A (talk) 14:54, 26 August 2021 (UTC)

I get the same; moreover, an exhaustive search with 1 ≤ p,q,r,s ≤ 25 finds nothing better, so suspicion can be upgraded to certainty.  --Lambiam 16:12, 26 August 2021 (UTC)

Thanx!Naraht (talk) 21:26, 26 August 2021 (UTC)

What would make a solution "better"? —Tamfang (talk) 00:19, 1 September 2021 (UTC)

A lower value for Z than 25 would be better than Z = 25.  --Lambiam 07:32, 1 September 2021 (UTC)