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MMO 363 Moscow MO 1957 sum of 8 consecutive Fibonacci

Source:

March 20, 2021
number theorySumSequenceFibonacci

Problem Statement

Eight consecutive numbers are chosen from the Fibonacci sequence 1,2,3,5,8,13,21,...1, 2, 3, 5, 8, 13, 21,.... Prove that the sequence does not contain the sum of chosen numbers.
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