In the modulo arithmetic ring $\mathbb{Z}_{17}$, compute the least non-negative residue of: $$(14 + …
What is the smallest single-digit positive integer $x$ such that the five-digit number $1234x$ …
Evaluate the sum of the first five prime numbers in $\mathbb{N}$.
Solve for $x$: $$x = 2^{2^3}$$ Hint: Is $2^{(2^3)}$ the same as $(2^2)^3$?
A checksum algorithm generates the base-10 integer $N = 458x2$, where $x$ is a …
Two celestial bodies orbit a star with periods of 12 and 18 local years, …
Evaluate the expression: $$\frac{2}{\sqrt{2}}$$
Solve for $x$: $$x = \ln(i)$$ Format: i*[fraction]
What is the last digit of $7^{2026}$?
Given two coprime token denominations of 7 and 12, what is the strictly largest …
In the context of public-key cryptography, find the unique modular multiplicative inverse $x \in …
Calculate the principal real value of $i^i$. Format: e^(-pi/X)
Evaluate $\phi(40)$, which represents the number of integers $k$ in the range $1 \le …
Solve: $$\cos(x) = i$$ Format: [fraction] - i ln([term])
Calculate the principal value for: $$\sin(x) = 2$$ Format: X/Y - i*Z
Calculate the exact number of trailing zeros in the decimal representation of $100!$ (100 …
Evaluate the exact sum of the infinite series: $$\sum_{n=1}^{\infty} \frac{1}{n^2}$$ Format: pi^2/X
Determine the least non-negative residue of $16! \pmod{17}$.