1. Multiples of 3 and 5 (1*)

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

Method 1: Set, union, sum, print

union : union is still a set operation, union([1,2],[2,3])=[1,2,3], even though we apply it on arrays.
println: print line, print the argument and start a new line.

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

while : while loop while condition body end
append!(collection, collection2): append collection 2 to collection, ! indicates collection will takes on the new value
last(coll): getting the last element of an ordered collection
iseven(x::Integer): test whether the integer x is even, and gives either 0 or 1 of type Bool
filter(f,a::AbstractArray): select elements from the array a base on the result of the boolean function f applying to each element of a

. : broadcasting, since A is an array, we want to broadcast the function iseven onto its elements
iseven.(A): gives an BitArray, with elements 0 or 1, e.g. iseven([1 2 3]) ----->[0 1 0]
A[ iseven.(A) ] : extract elements on positions with an 1 in the BitArray
$ : expression interpolation

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

using package: packages can be called with the using command
factor(n::Integer) : returns the prime factorization of the integer, e.g. factor(-9) returns -1 ⋅ 3^2
collect(collection): turn our collection into an array, in this case, we get an array of pairs, (arraye，exponent).

]

add package

rm package

update package

update

We can enter the Julia package management mode, by enter ] in REPL
add package: add and install package automatically
rm package : remove a package
update : update a given package, or if no name is supplied, all packages will be updated

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.

a==b: checks if a=b, and return 1 or 0
We then create a multiplication table M , and broadcast the function isPalindrome to all entries in M, and select the Palindromes
maximum(itr): find the maximum element in itr