Number Theory Basics Flashcards

Question 1

What does it mean for an integer $n$ to be even or odd?

Accepted Answer

Even: $n=2k$ for some integer $k$. Odd: $n=2k+1$ for some integer $k$.

Question 2

State the division algorithm.

Accepted Answer

For integers $a$ and $b>0$, there exist unique integers $q,r$ such that $a=bq+r$ with $0\le r<b$.

Question 3

State Fermat's Little Theorem.

Accepted Answer

If $p$ is prime and $p
mid a$, then $$a^{p-1}\equiv 1 \pmod p.$$ Equivalently, for any integer $a$, $$a^p\equiv a\pmod p.$$

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