Again, this factorization is almost unique.

同样，这种因式分解几乎是唯一的。

But unlike factorization, we need these problems to be so hard that they're even unbreakable with a quantum computer.

但与因式分解不同，我们需要这些问题非常难， 以至于它们甚至无法用量子计算机破解。

Well, remember how I mentioned that a factorization into gaussian primes can look different if you multiply some of them by i, -1 or -i?

好吧，还记得我曾，其中一些素数乘以 i、-1 或 -i，则分解为高斯素数可能看起来会有所不同吗？

And this problem, called " integer factorization, " is exactly what each of your smartphones and laptops is using right now to keep your data secure.

这个问题称为“整数因式分解”，正是您的每部智能手机和笔记本电脑现在正在使用的问题， 以确保您的数据安全。

We're looking for new, hard mathematical problems. We're looking for problems that, just like factorization, can be used on our smartphones and on our laptops today.

我们正在寻找新的、困难的数学问题。我们正在寻找可以在今天的智能手机和笔记本电脑上使用的问题，就像因式分解一样。

And the beauty of this Goodall number is you can do a prime factorization of it, and you can work out exactly what symbols made up this card.

古道尔数的美妙之处在于， 你可以对它进行质因数分解，然后就能准确地算出这张卡片是由哪些符号组成的。

But other than the things you can get by multiplying some of these factors by -1, i or -i, factorization within the Gaussian integers is unique.

但除了这些因子中的一些乘以 -1、i 或 -i 可以获得的结之外，高斯整数内的因式分解是唯一的。

So really, factorization in the integers is not perfectly unique, it's almost unique, with the exception that some of the factors might be multiplied by -1. Analogy with primes Factoring works very similarly in Gaussian integers.

所以实际上， 整数的因式分解并不是完全唯一的，它几乎是唯一的， 除了某些因子可能乘以 -1 之外。 与素数的类比 因式分解在高斯整数中的工作原理非常相似。