Recall the definition of the Fibonacci numbers: <br><pre>f1 := 1 <br>f2 := 2 <br>fn := f_n-1 + f_n-2 (n&gt;=3) </pre> <br>Given two numbers a and b, calculate how many Fibonacc…

Gustavo knows how to count, but he is just now learning how to write numbers. He has already learned the digits 1, 2, 3, and 4. But he does not yet realize that 4 is different than 1, so he thinks that 4 is just another way to write 1. He is having fun with a …

The <em>Stern-Brocot tree</em> is a beautiful way for constructing the set of all non-negative fractions <span class="MATH"><img src="/admin/../upload/pimg1532_1.png" alt="$ {m \over n}$" align="MIDDLE" border="0" height="25" width="17">…

<p>This problem seeks the coefficients resulting from the expansion of the polynomial</p> <p align="justify"></p> <div align="CENTER" class="mathdisplay"><i>P</i> = (<i>x</i>₁ + <i…

Given any integer 0 &lt;= n &lt;= 10000 not divisible by 2 or 5, some multiple of n is a number which in decimal notation is a sequence of 1's. How many digits are in the smallest such a multiple of n?

Stan and Ollie play the game of multiplication by multiplying an integer p by one of the numbers 2 to 9. Stan always starts with p = 1, does his multiplication, then Ollie multiplies the number, then Stan, and so on. Before a game starts, they draw an integer …