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ASU 313 All Soviet Union MO 1981 k_n<=n \sqrt n, (m-n) | (k_n - k_m)

Source:

July 23, 2019
number theorySequenceInteger sequence

Problem Statement

Find all the sequences of natural knk_n with two properties:
a) kn≤nnk_n \le n \sqrt {n} for all nn
b) (kn−km)(k_n - k_m) is divisible by (m−n)(m-n) for all m>nm>n
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