The Smallest kk

Let f(x)=7x11+11x7+9kxf(x)=7x^{11}+11x^{7}+9kx g(x)=7x13+13x7+10kxg(x)=7x^{13}+13x^{7}+10kx

Find the minimum positive value of kk for which 77f(x)77| f(x) and 91g(x)91|g(x) for every integer xx

Details and Assumptions

  • We use "\mid" to mean "divides evenly into". For example, 363\mid6, and 1213212\mid132.
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