MathDB

Let

k \ge 1

be an integer and

a_1, a_2, ... , a_k, b1, b_2, ..., b_k

rational numbers with the property that for any irrational numbers

x_i >1

i = 1, 2, ..., k

, there exist the positive integers

n_1, n_2, ... , n_k, m_1, m_2, ..., m_k

such that

a_1\lfloor x^{n_1}_1\rfloor + a_2 \lfloor x^{n_2}_2\rfloor + ...+ a_k\lfloor x^{n_k}_k\rfloor=b_1\lfloor x^{m_1}_1\rfloor +2_1\lfloor x^{m_2}_2\rfloor+...+b_k\lfloor x^{m_k}_k\rfloor

Prove that

a_i = b_i

for all

i = 1, 2, ... , k

Problem Statement