Timeline for Find integers $a, b, c, d, m, n, p$ so equation has six distinct solutions
Current License: CC BY-SA 4.0
10 events
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| Jan 15, 2020 at 8:00 | comment | added | Roman | @minhthien_2016 it looks like a tough problem. I suppose that to some extent, integer problems are internally solved by enumeration (after domain restrictions), which tend to scale exponentially with the number of unknowns. | |
| Jan 15, 2020 at 4:09 | comment | added | minhthien_2016 |
@Roman I tried this code f[x_] = Abs[(a x + b) (c x + d)] + Abs[m x + n] + p x^2 + q x ; Solve[Join[{Equal @@ f /@ {1, 2, 3, 4, -5, -4, -3, -2}, p != 0, a >= 1, c >= 1, b <= d}, Thread[-500 <= {a, b, c, d, m, n, q} <= 500]], {a, b, c, d, m, n, p, q}, Integers] my computer runs too long, about 1 h. I can not get result.
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| Jan 14, 2020 at 23:47 | comment | added | minhthien_2016 | @Roman How can I find all equations has 6 integer solutions x from 1 to 10? | |
| Jan 14, 2020 at 12:44 | history | edited | Roman | CC BY-SA 4.0 |
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| Jan 14, 2020 at 9:26 | vote | accept | minhthien_2016 | ||
| Jan 14, 2020 at 7:42 | history | edited | Roman | CC BY-SA 4.0 |
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| Jan 14, 2020 at 7:34 | comment | added | Roman | Thanks @Akku14, I've updated the answer to reflect the updated question. | |
| Jan 14, 2020 at 7:34 | history | edited | Roman | CC BY-SA 4.0 |
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| Jan 14, 2020 at 6:36 | comment | added | Akku14 |
These are all solutions with m == 0 . You get solutions with nonzero m if you enlarge the parameter range: Solve[{f[1] == 0, f[2] == 0, f[3] == 0, f[4] == 0, f[7] == 0, f[9] == 0, -100 <= a <= 100, -100 <= b <= 100, -100 <= c <= 100, -100 <= d <= 100, -100 <= m <= 100, -100 <= n <= 100, -100 <= p <= 100, m != 0}, {a, b, c, d, m, n, p}, Integers] or even +- 1000.
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| Jan 13, 2020 at 21:45 | history | answered | Roman | CC BY-SA 4.0 |