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Category Archives: Elementary Number Theory
Freshman’s Dream Come True! (But only in characteristic $p$)
A well-known fallacy committed by students is the so-called “Law of Universal Linearity” (the link is to a discussion of this phenomenon on Mathematics Stack Exchange). The most famous example of this is the statement $$\left(x+y\right)^n = x^n + y^n,$$ … Continue reading
Divisibility Rules: An Introduction to Modular Arithmetic
There are many rules for determining whether a number is divisible by another. For example, we know that a number is even (divisible by 2) whenever the one’s digit is even. We also know that a number is divisible by … Continue reading
Posted in Basic Facts, Elementary Number Theory
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