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Viet Nam TST 2010 Pro 1

Source:

October 24, 2010
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let nn be a positive integer. Let TnT_n be a set of positive integers such that: Tn={11(k+h)+10(nk+nh)∣(1≤k,h≤10)}{T_n={ \{11(k+h)+10(n^k+n^h)| (1 \leq k,h \leq 10)}}\} Find all nn for which there don't exist two distinct positive integers a,b∈Tna, b \in T_n such that a≡b(mod110)a\equiv b \pmod{110}
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