Show that for n > 1 we can find a polynomial p(a, b, c) with integer coefficients such that p(xn, xn+1, x + xn+2) ≡ x.
By playing with small n, we soon find a general pattern:
x = (x + xn+2)(1 - xn+1 + x2(n+1) - ... + (-1)n-2x(n-2)(n+1) ) + (-1)n+1(xn)n.
The proof is immediate.
33rd Putnam 1972
© John Scholes
27 Jan 2001