I could not understand the difference between these two (mod & rem) functions.
Clojuredoc's example for rem describes the difference:
;; rem and mod are commonly used to get the remainder.
;; mod means Gaussian mod, so the result is always
;; non-negative. Don't confuse it with ANSI C's %
;; operator, which despite being pronounced
;; 'mod' actually implements rem, i.e. -10 % 3 = -1.
user=> (mod -10 3)
2
user=> (rem -10 3)
-1