Learn how to solve challenging math coding problems and prep for your technical interview.

## 3 ways to check if a value is prime

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. Given an input value check if it's a prime.

## Finding all prime factors

Given a number, return all the prime factors and their corresponding number of occurrences.

## Project Euler Problem 46: Goldbach's other conjecture

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. For example,

`9 = 7 + 2 x 1`^{2}

15 = 7 + 2 x 2^{2}

21 = 3 + 2 x 3^{2}

25 = 7 + 2 x 3^{2}

27 = 19 + 2 x 2^{2}It turns out the conjecture was false. What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?

## Project Euler Problem 12: Highly divisible triangular number

The sequence of triangle numbers is generated by adding the natural numbers. So the

`7`triangle number would be^{th}`1 + 2 + 3 + 4 + 5 + 6 + 7 = 28`. The first ten terms would be:`1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...`Let us list the factors of the first seven triangle numbers:

`1: 1`

3: 1,3

6: 1,2,3,6

10: 1,2,5,10

15: 1,3,5,15

21: 1,3,7,21

28: 1,2,4,7,14,28We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

## Integer Right Triangles

If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120: {20,48,52}, {24,45,51}, and {30,40,50}.

## Pluses and Minuses 1-9

Write a program that outputs all possibilities to put + or - or nothing between the numbers 1

## Project Euler Problem 27: Quadratic Primes

Euler discovered the remarkable quadratic formula:

`n`^{2}+ n + 41It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 40

^{2}+ 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41^{2}+ 41 + 41 is clearly divisible by 41.The incredible formula

`n`was discovered, which produces 80 primes for the consecutive values^{2}− 79n + 1601`n = 0`to`79`. The product of the coefficients,`−79`and`1601`, is`−126479`.Considering quadratics of the form:

`n² + an + b, where |a| < 1000 and |b| < 1000`where

`|n|`is the modulus/absolute value of`n`e.g.`|11| = 11`and`|−4| = 4`Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes for consecutive values of

`n`, starting with`n = 0`.