Alex Chen '24
Modular Arithmetic 

 Modular Arithmetic is a very unintuitive concept for most people, as the base 10 system is very well entrenched in our brains and education system. However, modular arithmetic has a variety of uses that range from scheduling to banking to coding to cryptography. 

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What is Modular Arithmetic?

Simply put, Modular Arithmetic is a way of counting that is similar to how you would count on your fingers, which is what our current base 10 system is built on. For example, for base 9, instead of counting up to 9 and going to the next digit place, it goes up to 8 and then to the next digit place. Think of the highest digit being 8 for base 9, and for higher bases, we start to substitute letters and symbols to represent a certain number but as a single digit.

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Modular Arithmetic

Modular Arithmetic is essentially working with the remainder of two numbers. A/B = Q + remainder R/B. The function of A mod B is equal to R. This is most obvious when looking at the clock and time, whereupon you go from 1-12 o’clock in the morning, and subsequently loop back around after 12 to go to 1 o’clock in the afternoon again. In theory, so is the yearly calendar, whereupon reaching the 12th month, you go back to the first again.

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Uses

Modular Arithmetic has a variety of uses, from cryptography to scheduling, and is something that everyone needs to learn. It is one of the main points of number theory, and it is also useful for schedules, banking, and cryptography.