#Challenge (by Doron Zeilberger) to Manuel Kauers ($100 donation to the OEIS in your honor)
#PROVE RIGOROUSLY that the minimum of the following polynomial 
#in (x,y,z) in [0,infinity]^3 is 0

#----------------------
#UPDATE: Manuel Kauers met the challenge, see
# https://sites.math.rutgers.edu/~zeilberg/tokhniot/MKchallengeSolution.txt
#A donation to the OEIS was made by DZ
#-------------------------


P:=
16384*x^10*y^4*z^2+98304*x^10*y^3*z^3+221184*x^10*y^2*z^4+221184*x^10*y*z^5+
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33619968*x^9*y^2*z^5+31961088*x^9*y*z^6+11612160*x^9*z^7+1048576*x^8*y^6*z^2+
30375936*x^8*y^5*z^3+299171840*x^8*y^4*z^4+1182351360*x^8*y^3*z^5+2227322880*x^
8*y^2*z^6+2018801664*x^8*y*z^7+711327744*x^8*z^8+3293184*x^7*y^7*z^2+130433024*
x^7*y^6*z^3+1973133312*x^7*y^5*z^4+14045888512*x^7*y^4*z^5+48100549632*x^7*y^3*
z^6+84046629888*x^7*y^2*z^7+72816012288*x^7*y*z^8+24905180160*x^7*z^9+6838272*x
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