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### Mod

```
Date: 05/17/99 at 11:32:38
From: P. Grabowski
Subject: Mod

Hello!

I have been interested in math (something about prime numbers) but
can't find anywhere an explanation of what "mod" is. I am prevented
from learning more until I know what it means. Can you help to explain
it for me please? It comes in the line a^(p-1) = 1 mod p. Is it
something  like a remainder?

Thank you,
Grabowski
```

```
Date: 05/17/99 at 14:44:52
From: Doctor Rob
Subject: Re: Mod

Thanks for writing to Ask Dr. Math.

The sentence a = b (mod n) means that n is a divisor of a - b. This
sentence is read, "a is congruent to b modulo n."  It is something
like a remainder, because if you subtract a remainder from the
dividend, the divisor will go into the result evenly.

Examples: 100 = 86 (mod 7), because 100 - 86 = 14 has 7 as a divisor.
On the other hand, if you divide 100 by 7, the quotient is 14 and
remainder is 2, and 100 = 2 (mod 7), too.

If you need more explanation, write again.

- Doctor Rob, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

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