Divisible by 13
All natural numbers from 1 to 2006 are written on a sheet of paper, and a series of operations is performed as described below. At each step, any number of numbers are deleted from the list and their sum is denoted by S. Instead of the deleted numbers, a single number is added, which is the remainder obtained from the division of S by 13. After some number of such steps, only two numbers remain on the paper. One of them is 100. Find the other number.
Difficulty level (1 very easy - 10 very hard): 3
Topics:
Number Theory
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Modular Arithmetic / Remainder Arithmetic
Number Theory
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Division
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Parity (Even/Odd)
Algebra
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Sequences
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Arithmetic Progression / Arithmetic Sequence
- Grossman Math Olympiad, 2006 Question 2
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