$63^{63^{63}} \mod 100$
4972
Mod of numbers with large exponents [modular order reduction]
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
95033
Find the remainder of a number with a large exponent
138696
Last two and three digits of $7^{754}$
123544
Show that $n = 3^{100} + 2$ is not a prime number.
156956
Give the remainder of $x^{100}$ divided by $(x-2)(x-1)$.
112080
Proving the Product Rule for exponents with the same base
64592
The last two digits of $9^{9^9}$
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
72406
Last two digits of $2^{1000}$ via Chinese Remainder Theorem?
109640
How do i find $(1+i)^{100}?$
109490
Modular arithmetic problem (mod $13$)
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
92518
mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
58803
${n \choose k} \bmod m$ using Chinese remainder theorem?
143510
Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
156032
Find a such that $112_a$, $63_a$ and $34_a$ are in an arithmetic progression