# it is thought that there are only five Fibonacci numbers that are also triangular numbers. Find them.

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Expert Answers

justaguide | Certified Educator

Does this list end with 5 numbers, is there a proof that it couldn't continue indefinitely.

Student Comments

llltkl | Student

In 1989, L. Ming proved the only Fibonacci numbers which are triangular are 1, 3, 21, and 55. Please refer to Ming, L. "On Triangular Fibonacci Numbers." *Fib. Quart.* **27**, 98-108, 1989.

llltkl | Student

The Fibonacci Sequence is the series of numbers:

0,1,1,2,3,5,8,13,21,34,55,89..............

The next number is found by adding up the two numbers before it.

The general formula is `T_n=T_(n-1)+T_(n-2)`

On the other hand, the Triangular Number Sequence is:

1,3,6,10,15,21,28,36,45,55,.......where `T_n=(n(n+1))/2.`

Five Fibonacci numbers that are also triangular numbers are **1,1,3,21,55.**