. Modular Arithmetic In a clock, we use the numbers to to represent the time period of hours. How is it possible to represent the hours of a day in a number format? We use , , , , , , , , , , , and after , we use instead of and instead of and so on.
That is after we again start from , , ,... In this system the numbers wrap around to . This type of wrapping around after hitting some value is called Modular Arithmetic . In Mathematics, modular arithmetic is a system of arithmetic for integers where numbers wrap around a certain value.
Unlike normal arithmetic, Modular Arithmetic process cyclically. The ideas of Modular arithmetic was developed by great German mathematician Carl Friedrich Gauss , who is hailed as the “Prince of mathematicians” . Examples . The day and night change repeatedly.
. The days of a week occur cyclically from Sunday to Saturday. . The life cycle of a plant.
. The seasons of a year change cyclically. (Summer, Autumn, Winter, Spring) . The railway and aeroplane timings also work cyclically.
The railway time starts at : and continue. After reaching : , the next minute will become : instead of : . Fig. .
Life Cycle of Plant Fig. . Numbers and Sequences . .
Congruence Modulo Two integers a and b are congruence modulo n if they differ by an integer multiple of n . That a kn for some integer k . This can also be written as a º (mod n ). Here the number n is called modulus.
In other words, a º (mod n ) means a - is divisible by n . For example, º (mod ) because –