Математика за програмисти-домашно

Problem 1.	Some Primes
Find the 24th, 101st and 251st prime number.

Solution:
	24th=89
	101st=547
	251st=1597
=================================================
Problem 2.	Some Fibonacci Primes
Check if the 24th, 101st and 251st prime numbers are part of the base Fibonacci number set. What is their position?

Solution:
Prime position = number = Fibonacci number set position
	24th=89=11
	101st=547= is not part of the base Fibonacci number set
	251st=1597=17
=================================================
Problem 3.	Some Factorials
Find 100!, 171! and 250! Give all digits.

Solution:
	100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
	171! = 1241018070217667823424840524103103992616605577501693185388951803611996075221691752992751978120487585576464959501670387052809889858690710767331242032218484364310473577889968548278290754541561964852153468318044293239598173696899657235903947616152278558180061176365108428800000000000000000000000000000000000000000
	250! = 3232856260909107732320814552024368470994843717673780666747942427112823747555111209488817915371028199450928507353189432926730931712808990822791030279071281921676527240189264733218041186261006832925365133678939089569935713530175040513178760077247933065402339006164825552248819436572586057399222641254832982204849137721776650641276858807153128978777672951913990844377478702589172973255150283241787320658188482062478582659808848825548800000000000000000000000000000000000000000000000000000000000000
=================================================
Problem 4.	Calculate Hypotenuse
You are given three right angled triangles. Find the length of their hypotenuses.

1.	Catheti: 3 and 4
Solution:
	Hypotenuses = 5
2.	Catheti:  10 and 12
Solution:
	Hypotenuses = 15.6204993518
3.	Catheti 100 and 250
Solution:
	Hypotenuses = 269.258240357
=================================================
Problem 5.	Numeral System Conversions

Convert 1234d to binary and hexadecimal numeral systems.
	Solution: 1234d = 10011010010b = 4D2hex
Convert 1100101b to decimal and hexadecimal numeral systems.
	Solution: 1100101b = 101d = 65hex
Convert ABChex to decimal and binary numeral systems.
	Solution: ABChex = 2748d = 0000101010111100b
=================================================
Problem 6.	Least Common Multiple
Find LCM(1234, 3456).

Solution:
	For the values: 1234, 3456
	The LCM is: 2132352
=================================================
Sources for all solutions:
https://www.google.com
http://www.calculatorsoup.com/
http://www.numberempire.com/
https://www.wolframalpha.com
http://www.rapidtables.com/
http://www.miniwebtool.com/hypotenuse-calculator/