struct IntMod{N} <:Integer
    val::Int64
    function IntMod{N}(y) where {N}
        y%=N
        y>0 ? y=y : y = N+y
        return new(y)
    end
end

IntMod{N}(y::IntMod{N}) where {N} = y

Base.:+(x::IntMod{N}, y::IntMod{N}) where {N} = IntMod{N}(x.val+y.val)
Base.:-(x::IntMod{N}, y::IntMod{N}) where {N} = IntMod{N}(x.val-y.val)
Base.:*(x::IntMod{N}, y::IntMod{N}) where {N} = IntMod{N}(x.val*y.val)
Base.:/(x::IntMod{N}, y::IntMod{N}) where {N} = x*inv(y)
Base.show(io::IO, x::IntMod{N}) where {N} = print(io, x.val," mod ", N)

Modulus(x::IntMod{N}) where {N} = N

macro intmod(x, N)
    return :(IntMod{$N}($x))
end

## from Rosetta Code
φ(n) = sum(1 for k in 1:n if gcd(n, k) == 1)
is_prime(n) = φ(n) == n - 1

@generated function Base.inv(x::IntMod{N}) where {N}
    if is_prime(N)
        return :(IntMod{N}(gcdx(x.val, $N)[2]))
    else
        return :(throw(DomainError(x, "N is not prime")))
    end
end