Plz help me with my maths

I don't know how to do these questions,can you help me?

1.Each bag of candies has 20 pieces.Suppose you want to buy candies such that after keeping 3 pieces for yourself,you can evenly distribute the rest among 49 children.What is the minimum number of bags of candies you should buy?

2.Suppose ka=kb(mod n).Prove that if gcd(k,n)=1,than a=b(mod n)

3.If gcd(x,y)=1 and xy is divisible by a prime z,than either x is divisible by z or y is divisible by z but not both (you can use prime factorization)

4.Let a and b positive numbers such that a>b and gcd(a,b)=1
i)Show that for 1=<a-1 ,ib not=0(mod a)
ii)Show that for 1=<i<j=<a-1 ,ib not=jb(mod a)
iii)Using(ii),show that we can find k such that kb=1(mod a)

5.Explain why the Extended Euclidean Algorithm works.

Thank you for your help