🔢 number theory

1. The problem gives an arithmetic expression $7 2 9 8 - 3 1 8 + 8 5$ represented in a positional numeral system with radix (base) 9. 2. We first interpret the numbers separated by

1. Find the values of x and y for $(a,b)=(81,57)$ using the Extended Euclidean Algorithm. Step 1: Compute $\gcd(81,57)$ using the Euclidean Algorithm:

### Exercice 18 1. Décomposer $a=118800$ et $b=12600$ en produit de facteurs premiers.

1. The problem is to understand and interpret the given formula: $$\zeta(s) \approx \sum_{n=1}^{V} \frac{1}{n^s} + \beta(V,s) \cdot V^{1-s}$$

1. **State the problem:** We have a positive integer $n$ with exactly 6 positive divisors. We list all positive divisors $d$ of $n$ and compute $\frac{n}{d}$ for each divisor $d$.

1. The problem appears to be evaluating or verifying the expression involving the numbers 10, 2, and 10 yielding the result 2. 2. However, the expression written as "10,2,10 = 2" i

1. Problem 33: Find the number of distinct incongruent solutions to $$98x \equiv 175 \pmod{49}$$. Step 1: Simplify the congruence. Note that $49$ divides both sides since modulo $4

1. The problem "How to solve 233" is ambiguous as 233 is a number, not an equation or a problem. 2. To clarify, if you want to find factors of 233, we can determine if 233 is prime

1. Let's state the problem: We want to prove or use Euler's theorem, which states that for any integer $a$ and $n$ that are coprime (\gcd(a,n)=1), $$a^{\phi(n)} \equiv 1 \pmod{n}$$

1. **Stating the problem:** The problem is about the Collatz conjecture, which says: start with any positive integer $n$. If $n$ is even, divide it by 2. If $n$ is odd, replace it

1. The problem described is a famous unsolved problem in mathematics known as the Collatz conjecture or 3n+1 problem. 2. The rule is: for a given starting positive integer $n$, if

1. The statement says: "There is a positive integer that is less than or equal to every positive integer." This means we're looking for a positive integer $n$ such that for every p