In computer programming, I use the mod operation to get the remainder from division, which can be used for many things, such as to check whether a number is even or odd. Is it allowed to use the mod operation in mathematics, or is it only in programming? If so, what is the proper way to write it (do I write something like 3 mod 2 or 3 % 2)? If not, is there a mathematical formula that will get the remainder from division?
Is it allowed to use the modulo operation in math
algebra-precalculuscomputer sciencenotation
Best Answer
The notation is $$a\equiv b \pmod c $$ which stands for $c$ divides $a-b$
For example $$27\equiv 2\pmod 5$$
It is a mathematical tool which is helpful in solving number theory problems.
For example you may use $ \pmod 5 $ arithmetics to show that every fifth term in the Fibbonaci's sequence,$$1,1,2,3,5,8,13,21,34,55,... $$ is divisble by $5$
The sequence in $\pmod 5$ turns out to be $$1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1,0,1,1,....$$ We are done!