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Definition

A **Giuga number** is a composite number **n** which is such that each of its distinct prime factors
**f** divide (n/f - 1) exactly.

All known Giuga numbers are even though it is not known for certain that there are no odd examples.

Example

30 is a Giuga number because its distinct prime factors are 2, 3 and 5 and:

* 30/2 - 1 = 14 is divisible by 2
* 30/3 - 1 = 9 is divisible by 3
* 30/5 - 1 = 5 is divisible by 5

Task

Determine and show here the first four Giuga numbers.

Stretch

Determine the fifth Giuga number and any more you have the patience for.

References

* Wikipedia: Giuga number
* OEIS:A007850 - Giuga numbers
assistant
```
my @primes = (3..60).grep: &is-prime;

print 'First four Giuga numbers: ';

put sort flat (2..4).map: -> $c {
    @primes.combinations($c).map: {
        my $n = [×] 2,|$_;
        $n if all .map: { ($n / $_ - 1) %% $_ };
    }
}

```

Output:

```
First 4 Giuga numbers: 30 858 1722 66198
```