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p(n)= only digits 1 - All-Russian MO 1994 Regional (R4) 9.3

Source:

August 26, 2024
number theoryDigitstrinomial

Problem Statement

Does there exist a quadratic trinomial p(x)p(x) with integer coefficients such that, for every natural number nn whose decimal representation consists of digits 11, p(n)p(n) also consists only of digits 11?
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