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euler_project.h
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euler_project.h
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/*
declares the problems past and present being worked on, aswell as
information about each task.
*/
#include <sys/types.h>
#include <inttypes.h>
#include "err_handle/err_handle.h"
#include "floatConsts.h"
/* header functions */
/* Example: If we list all the natural number below 10 that are multiples of 3
or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Problem: Find the sun of all the multiples of 3 or 5 below 1000. */
void prob1();
/* Each new term in the Fibonacci squence is generated by adding the previous
two terms. By starting with 1 and 2, the first 10 terms will be:
1,2,3,4,8,13,21,34,55,89,...
By considering the terms in teh Fibonacci sequence whose values do not
exceed four million, find the sum of the even-valued terms. */
void prob2();
/* The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime facor of the number 600851475143. */
void prob3();
/* A palindromic number reads the same both ways. The largest palindrome made
from the product of two 2-digit numbers is 9009 = 91 × 99.
Find the largest palindrome made from the product of two 3-digit numbers. */
void prob4();
/* 2520 is the smallest number that can be divided by each of the numbers from
1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the
numbers from 1 to 20? */
void prob5();
/* (1)The sum of the squares of thefirst ten natural numbers is,
1^2 + 2^2+...+10^2 = 385
(2)The square of thesum of the first ten natural numbers is,
(1 + 2 +...+10)^2 = 55^2 = 3025
Hence the difference between (1)the sum of the squares of the first ten natural
numbers and (2)the square of the sum is,
3025 - 385 = 2640
Find the difference between the sum of the square of the first one hundred
natural numbers and the square of the sum.
-Do examples but with 1-100 */
void prob6();
/* By listing the first six prime numbers: 2, 3, 5, 7, 11 and 13, we can see
that the 6th prime is 12.
What is the 10,001st prime number? */
void prob7();
/* The four adjacent digits in the 1000-digit number that have the greatest
product are 9 × 9 × 8 × 9 = 5832.
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
Find the thirteen adjacent digits in the 1000-digit number that have the
greatest product. What is the value of this product? */
void prob8();
/* A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2
For example, 3^2 + 4^2 = (9 + 16)
= 25
= 5^2.
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc. */
void prob9();