query: Two questions about $a^{2^{n-1}} \mod {2^{n}}$ and Fermat's Little Theorem
positive_passages.docid: 152039
positive_passages.text: Prove that $a^{2^n}=1 \mod 2^{n+2}$
negative_passages.docid: 19500
negative_passages.text: How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
negative_passages.docid: 50041
negative_passages.text: Significance of $\sqrt[n]{a^n} $?!
negative_passages.docid: 158684
negative_passages.text: How to solve and see resolution of $13^{53} \pmod 7$ using Fermat little Theorem?
negative_passages.docid: 21986
negative_passages.text: What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
negative_passages.docid: 9302
negative_passages.text: Questions about Divisibility of $2^n$ by $3$
negative_passages.docid: 35167
negative_passages.text: Prove congruence using fermat's thm
negative_passages.docid: 109224
negative_passages.text: Accumulation points of $\{ 2^{-n} + 5^{-m} : n,m \geq 1 \}$
negative_passages.docid: 48081
negative_passages.text: Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
negative_passages.docid: 24572
negative_passages.text: Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
negative_passages.docid: 16697
negative_passages.text: Fermat Last Theorem for non Integer Exponents
negative_passages.docid: 157711
negative_passages.text: Number Theory: Prove that $m | \phi(a^m - 1)$
negative_passages.docid: 79219
negative_passages.text: Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
negative_passages.docid: 43048
negative_passages.text: When is $2^n \pm 1$ a perfect power
negative_passages.docid: 32136
negative_passages.text: How to prove Lucas's Converse of Fermat's Little Theorem without using primitive root?
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 6332
negative_passages.text: If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined