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Bifonacci (Posted on 2019-02-19)

How many pairs of Fibonacci numbers each less than than 10⁸ have a greatest common divisor equal to 233?

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 2

233 is prime, so any pair must each have 233 as the sole common factor. The only Fibonacci numbers in the range with 233 as a factor are

F13=233

F26=121393=233*521

F52=63245986=2*233*135721

Any pair of these will work, so the answer is 3.

Posted by Jer on 2019-02-19 09:38:28

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