And then the remainder, 358, I'll just say the remainder.

然后余数，358，我说余数。

There's no " remainder, " we would say.

我们会说，没有“余数”。

Remainder. The next word is remainder.

余。 下一个词余数。

Your " remains" (remains) refer to what's left of your body.

你的“余数”（remains）指的你身体剩下的部分。

This code calculated the remainder if we divide 5 into 11, which is one.

这段代码计算了 5 除以 11 的余数，11 1。

So too, at the present time there is a remnant chosen by grace.

如今也这样，照着拣选的恩典，还有所留的余数。

The hard part is figuring out the exponent given only the result and the base.

重点，如果只给余数和基数，很难得知指数多少。

" 10 divided by 4" gives you 2 with a remainder of 2, so: " 2 remainder 2" .

所以：“10 除以 4” 得到 2，余数为 2， 所以：“2 余数 2” 。

So if you add up this leg and this leg-- so this plus that leg is going to be the remainder.

因此，如果您将这条和这条相加——那么这条加上那条余数。

The word " residue" here is sort of an overdramatic way of saying remainder and mod means something like where the thing you divide by is.

这里的“余数”这个词一种夸张的余数表达方式，而 mod 的意思你除以的东西在哪里。

The factors of 710 are 71, 5 and 2. So if the remainder or residue is divisible by any of those then so is the number.

710 的因数 71、5 和 2。因此，如果余数或余数可被其中任何一个整除，则该数字也能整除。

This means taking one number, the base, to the power of another number, the exponent, and taking the remainder when dividing by a third number, the modulus.

这意味着取一个数（底数）的另一个数（指数）的次方，并在除以第三个数（模数）时取余数。

If I tell you I raised 3 to some secret number, modulo 31, and got 7 as the remainder, you'd have to test a lot of exponents to know which one I picked.

如果我告诉你我将 3 加到某个秘密数字上，对 31 取模，然后得到 7 作为余数，你必须测试很多指数才能知道我选择了哪一个。

To phrase it with our fancier language, each of these spiral arms shows a residue class mod 44. And maybe now you can tell me what happens when we limit our view to prime numbers.

用我们更奇特的语言来表达它，个旋臂都显示了一个余数类 mod 44。 也许现在你可以告诉我当我们将我们的视野限制在素数时会发生什么。

So, for example, if we wanted to calculate 3 to the 5th power, modulo 31, we would calculate 3 to the 5th, which is 243, then take the remainder when divided by 31, which is 26.

因此，例如，如果我们想计算 3 的 5 次方，模 31，我们将计算 3 的 5 次方，即 243，然后取余数除以 31，即 26。

Which tells us that everything else combined-- so if you take this yellow portion right here and this yellow portion right here, so everything beyond 2 standard deviations in either direction-- that has to be the remainder.

这告诉我们其他所有东西都加起来了——所以如果你把这个黄色部分和这个黄色部分放在一起，那么在任何一个方向上超过 2 个标准差的所有东西——那余数。

If the number of steps in the distance between the cabinet-door and the arm-chair will divide by three without a remainder, then the new regimen will cure him; but if it does not so divide, then it will not.

如果柜门到扶手椅之间的步数除以三没有余数，那么新的治疗方法会治愈他；但如果它不那么分裂，那么它不会分裂。