And I wouldn't have noticed it except for this factorization.

若非这次因式分解，我本不会察觉到这一点。

Again, this factorization is almost unique.

再次强调，这种分解几乎是唯一的。

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?

还记得我提到过，如果你将一些斯素乘以i、-1或-i，它们的分解形式可能会不同吗？

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。

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.

但除了将这些因子中的一些乘以 -1、i 或 -i 可以获得的结果外，斯整内的因式分解是唯一的。

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.

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

Covarnet uses mathematical techniques like non-negative matrix factorization to find groups of cell subsets that often appear together, and then correlation analysis to map out the likely connections within those groups.

Covernet利用非负矩阵分解技术，识别出经常共同出现的细胞亚群组合，再通过相关性分析，绘制出这些组合内部的潜在关联。