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find smallest t such that 11 | a_t , where a_n=12345678091011...n

Source: Czech-Polish-Slovak Junior Match 2014, Individual p4 CPSJ

March 13, 2020
number theorydividesdivisibleDigits

Problem Statement

The number ana_n is formed by writing in succession, without spaces, the numbers 1,2,...,n1, 2, ..., n (for example, a11=1234567891011a_{11} = 1234567891011). Find the smallest number t such that 11∣at11 | a_t.
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