Computational Mathematics

John Rhodes
August 15, 2023
Computational Mathematics

Hyperexponentiation

The hyperexponentiation or tetration of a number $a$ by a positive integer $b$, denoted by $a\mathbin{\uparrow \uparrow}b$ or $^b a$, is recursively defined by: $a \mathbin{\uparrow \uparrow}...

John Rhodes
August 15, 2023
Computational Mathematics

Semiprimes

A composite is a number containing at least two prime factors. For example, $15 = 3 \times 5$; $9 = 3 \times 3$; $12 = 2 \times...

John Rhodes
August 15, 2023
Computational Mathematics

Here are the records from a busy telephone system with one million users: RecNrCallerCalled $1$$200007$$100053$$2$$600183$$500439$$3$$600863$$701497$$\cdots$$\cdots$$\cdots$ The telephone number of the caller and the called number in record...

John Rhodes
August 15, 2023
Computational Mathematics

Number Mind

The game Number Mind is a variant of the well known game Master Mind. Instead of coloured pegs, you have to guess a secret sequence of digits....

John Rhodes
August 15, 2023
Computational Mathematics

Triangles Containing the Origin

Consider the set $I_r$ of points $(x,y)$ with integer co-ordinates in the interior of the circle with radius $r$, centered at the origin, i.e. $x^2 + y^2...

John Rhodes
August 15, 2023
Computational Mathematics

Maximum Product of Parts

Let $N$ be a positive integer and let $N$ be split into $k$ equal parts, $r = N/k$, so that $N = r + r + \cdots...

John Rhodes
August 15, 2023
Computational Mathematics

RSA Encryption

The RSA encryption is based on the following procedure: Generate two distinct primes $p$ and $q$.Compute $n = pq$ and $\phi = (p – 1)(q – 1)$....

John Rhodes
August 15, 2023
Computational Mathematics

Grouping Two Different Coloured Objects

Having three black objects B and one white object W they can be grouped in 7 ways like this: (BBBW)(B,BBW)(B,B,BW)(B,B,B,W) (B,BB,W)(BBB,W)(BB,BW) In how many ways can sixty...