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a_n<K(1.01)^n

Source: 2013 China TST Quiz 2 Day 1 P2

March 31, 2013
limitmodular arithmeticquadraticsnumber theory proposednumber theory

Problem Statement

Prove that: there exists a positive constant KK, and an integer series {an}\{a_n\}, satisfying: (1)(1) 0<a1<a2<⋯<an<⋯0<a_1<a_2<\cdots <a_n<\cdots ; (2)(2) For any positive integer nn, an<1.01nKa_n<1.01^n K; (3)(3) For any finite number of distinct terms in {an}\{a_n\}, their sum is not a perfect square.
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