2007 iTest Problems/Problem 53
The following problem is from the Ultimate Question of the 2007 iTest, where solving this problem required the answer of a previous problem. When the problem is rewritten, the T-value is substituted.
Problem
Three distinct positive Fibonacci numbers, all greater than , are in arithmetic progression. Let be the smallest possible value of their sum. Find the remainder when is divided by .
Solution
By definition, for a Fibonacci number, and . From the definition, . That means the numbers , , and are in arithmetic progression with common difference .
Writing out the Fibonacci numbers, the first numbers that come after are , , , and . That means the desired three numbers are , , and . The sum of the three numbers is , and the remainder after dividing by is .
See Also
2007 iTest (Problems, Answer Key) | ||
Preceded by: Problem 52 |
Followed by: Problem 54 | |
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