# chickadee » math » mod=

##### Identifier search
mod= a b ...procedure
mod< a b ...procedure
mod<= a b ...procedure
mod> a b ...procedure
mod>= a b ...procedure
a
integer
b
integer

Each of these is equivalent to (op (mod a) (mod b) ...), where op is the corresponding numeric comparison function. Additionally, when given one argument, the inequality tests always return #t.

Suppose we wanted to know why 17/4 = 8 (mod 15), but 51/12 (mod 15) is undefined, even though normally 51/12 = 17/4. In code,

```> (with-modulus 15 (mod/ 17 4))
8
> (/ 51 12)
17/4
> (with-modulus 15 (mod/ 51 12))
Error: (modular-inverse) bad argument type - not coprime to modulus 15: 12```

We could try to divide by brute force: find, modulo 15, all the numbers a for which (mod* a 4) is 17, then find all the numbers b for which (mod* a 12) is 51.

```(import srfi-42)
> (with-modulus 15
(list-ec (:range a 15)
(if (mod= (mod* a 4) 17))
a))
(8)
> (with-modulus 15
(list-ec (:range a 15)
(if (mod= (mod* a 12) 51))
a))
(3 8 13)```

So the problem isn't that b doesn't exist, it's that b isn't unique.