# Computation Workshop Solution Checker

## Fibonacci Multiples

The sequence $$1, 1, 2, 3, 5, \ldots$$ is called the Fibonacci Sequence. It is the sequence $$f(1)$$, $$f(2)$$, $$f(3)$$, $$f(4)$$, $$\ldots$$ defined by

• $$f(1) = 1$$,
• $$f(2) = 1$$, and
• $$f(n + 2) = f(n + 1) + f(n)$$ for all $$n \ge 1$$.

So for example $$f(12) = 144$$.

Part A Determine the smallest positive integer $$a$$ such that $$F_a$$ is a multiple of $$100$$. Determine the smallest positive integer $$b$$ such that $$F_b$$ is a multiple of $$103$$. Determine the smallest positive integer $$c$$ such that $$F_{c-1}$$ is a multiple of $$100$$ and $$F_{c+1}$$ is a multiple of $$103$$.

## Hexagonal Squares

The square numbers $$(1, 4, 9, 16, 25, \ldots$$ are the numbers which can be arranged to make a square array of dots. Analogously, the Hexagonal numbers $$(1, 7, 19, 37, \ldots$$ are the numbers which can be arranged to make a hexagonal array of dots. A "Hexagonal-Square" is any positive integer which is both a Hexagonal number and a Square number. So for example $$1$$ is the first (smallest) Hexagonal-Square.

Part A What is the second Hexagonal-Square? What is the sum of the first $$6$$ Hexagonal-Squares? What is the square root of the tenth Hexagonal-Square?