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From: Artur on 26 Dec 2009 19:11
P.S.
I'm apologize but I don't know how to force this condition in
Mathematica variable "a" have to be root of polynomial order not higher as 4
That finding Mathematica solution:
{Root[93729137781599188892101109375 + 694786929294636041346875*x -
7512992033452287500*x^2 - 667145231722500*x^3 - 2495181500*x^4 +
29880*x^5 + x^6],k=-2,n=-1
have too high degree of polynomial for "a"

Artur



Artur pisze:
> Dear Mathematica Gurus,
> Who have idea how to change my procedure to find any resolution
> following problem in reasonable time:
>
> FindInstance[
> a^6 - 5000 a^5 k^4 + 15625000 a^4 k^8 - 39062500000 a^3 k^12 +
> 61035156250000 a^2 k^16 - 346851348876953125 a k^20 +
> 574052333831787109375 k^24 - 152587890625 a^3 k^11 n +
> 381469726562500 a^2 k^15 n - 715255737304687500 a k^19 n +
> 1192092895507812500000 k^23 n + 25000 a^5 k^2 n^2 -
> 117187500 a^4 k^6 n^2 + 183105468750 a^3 k^10 n^2 -
> 274658203125000 a^2 k^14 n^2 + 95367431640625000 a k^18 n^2 +
> 2740025520324707031250 k^22 n^2 + 5000 a^5 k n^3 -
> 34375000 a^4 k^5 n^3 + 23437500000 a^3 k^9 n^3 -
> 1912231445312500 a^2 k^13 n^3 + 4634094238281250000 a k^17 n^3 +
> 4118859767913818359375 k^21 n^3 - 120 a^5 n^4 +
> 101281250 a^4 k^4 n^4 - 787626953125 a^3 k^8 n^4 -
> 172827148437500 a^2 k^12 n^4 + 3451194763183593750 a k^16 n^4 +
> 6292783260345458984375 k^20 n^4 + 66406250 a^4 k^3 n^5 -
> 616455078125 a^3 k^7 n^5 + 256347656250000 a^2 k^11 n^5 +
> 6629085540771484375 a k^15 n^5 +
> 27122914791107177734375 k^19 n^5 - 2500000 a^4 k^2 n^6 -
> 1519921875000 a^3 k^6 n^6 + 433349609375000 a^2 k^10 n^6 +
> 5464096069335937500 a k^14 n^6 +
> 38636028766632080078125 k^18 n^6 - 20031250 a^4 k n^7 -
> 341732421875 a^3 k^5 n^7 - 1894716796875000 a^2 k^9 n^7 +
> 8129505920410156250 a k^13 n^7 +
> 93564096450805664062500 k^17 n^7 + 3131000 a^4 n^8 -
> 156031718750 a^3 k^4 n^8 - 9313589208984375 a^2 k^8 n^8 +
> 29971120880126953125 a k^12 n^8 +
> 81764254665374755859375 k^16 n^8 - 311220703125 a^3 k^3 n^9 -
> 5139099121093750 a^2 k^7 n^9 + 20748748779296875000 a k^11 n^9 +
> 58457677841186523437500 k^15 n^9 - 31638281250 a^3 k^2 n^10 -
> 1204147216796875 a^2 k^6 n^10 +
> 25867360687255859375 a k^10 n^10 +
> 97581827449798583984375 k^14 n^10 - 135380390625 a^3 k n^11 +
> 121599628906250 a^2 k^5 n^11 + 10643425646972656250 a k^9 n^11 +
> 95619381858825683593750 k^13 n^11 - 12457191250 a^3 n^12 -
> 465429111718750 a^2 k^4 n^12 + 7125597748291015625 a k^8 n^12 +
> 176131518226318359375000 k^12 n^12 -
> 1778971484375000 a^2 k^3 n^13 + 15609765167236328125 a k^7 n^13 +
> 123960684261322021484375 k^11 n^13 -
> 427022263671875 a^2 k^2 n^14 + 5523702651367187500 a k^6 n^14 +
> 62895859558105468750000 k^10 n^14 - 52864657812500 a^2 k n^15 +
> 5566817182763671875 a k^5 n^15 +
> 69470368091003417968750 k^9 n^15 + 3181330525000 a^2 n^16 +
> 755323840091796875 a k^4 n^16 +
> 50732234374265136718750 k^8 n^16 +
> 642590379882812500 a k^3 n^17 +
> 80834913409423828125000 k^7 n^17 +
> 887537465068359375 a k^2 n^18 +
> 35437872300158691406250 k^6 n^18 - 104724578519531250 a k n^19 +
> 8127588989220458984375 k^5 n^19 - 292795052411778125 a n^20 -
> 2870696813570914062500 k^4 n^20 +
> 491998345646972656250 k^3 n^21 +
> 1722637521892656250000 k^2 n^22 + 201732679018423828125 k n^23 +
> 43107630657534703125 n^24 == 0 && k != 0, {a, k, n}, Reals]
>
> Merry Christmas and Happy New Year
> Artur
>
>

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