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f_A(N) is the number of different solutions to linear diop.

Source: Spain MO 2010

February 11, 2011
number theory proposednumber theory

Problem Statement

Let pp be a prime number and AA an infinite subset of the natural numbers. Let fA(n)f_A(n) be the number of different solutions of x1+x2+…+xp=nx_1+x_2+\ldots +x_p=n, with x1,x2,…xp∈Ax_1,x_2,\ldots x_p\in A. Does there exist a number NN for which fA(n)f_A(n) is constant for all n<Nn<N?
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