local int = require "int"
local fmt = require "fmt"

local function is_curzon(n, k)
    local r = k * n
    return int.modpow(k, n, r+1) == r
end

for k = 2, 10, 2 do
    print($"The first 50 Curzon numbers with base {k}:")
    local n = 1
    local count = 0
    while count < 50 do
        if is_curzon(n, k) then
            fmt.write("%4d ", n)
            count += 1
            if count % 10 == 0 then print() end
        end
        n += 1
    end
    while true do
        if is_curzon(n, k) then count += 1 end
        if count == 1000 then break end
        n += 1
    end
    fmt.print("\nOne thousandth: %s\n", fmt.int(n))
end