1.Suppose that a,b∈Z are coprimes.

1)Show that gcd(a+b,a−b)∈{1,2}.

2)Show that gcd(a+b,a⋅b)=1.

2.I have 4.45 dollars in my pocket composed entirely of dimes (0.1 dollars) and quarters (0.25 dollars). What are the maximal and minimal number of coins that I can have? Can I have an equal amount of quarters and dimes?

3.Let n∈N

1）Show that ϕ(n^2)=nϕ(n)

2）Show that ϕ(n)≠n/4