New posts in Elementary Number Theory

Four Number Theorem : Let $a$, $b$, $c$, $d$ be integers such that $ab = cd$.

Given that $f(x)$ is a polynomial of degree $3$, and its remainders are $2x - 5$ and $-3x + 4$ when divided by $x^2 - 1$ and $x^2 - 4$ respectively.

Is it true that $\sum_{i=0}^{n-1} 2^i$ divides $\sum_{i=n}^{2n-1} 2^i$?

Find odd primes $p$ and $q$ such that $(p-1)\mid {3q-1}$ and $(q-1)\mid{3p-1}$.

If the largest positive integer is n such that $\sqrt{n - 100} + \sqrt{n + 100}$ is a rational no. , find the value of $\sqrt{n - 1}$ .

calculate the Integer solutions of an equation

Find all positive integers $x$ and $y$ for which $\frac{1}{x} + \frac{1}{y} = \frac{1}{p}.$

How to prove divisibility by $7$?

$2^{3^{n}}+1=(2+1)\left(2^{2}-2+1\right)\left(2^{2 \cdot 3}-2^{3}+1\right) \cdots\left(2^{2 \cdot 3^{n-1}}-2^{3^{n-1}}+1\right)$

Integer solutions of $2a+2b-ab\gt 0$