🔢 number theory

1. The problem asks us to find numbers with rotational symmetry of order 2, meaning when rotated 180 degrees, the digits look the same. 2. We analyze digits 0-9 for rotational symm

1. The problem asks to classify the number $-1$ by choosing the correct types of numbers it belongs to. 2. First, recall the definitions:

1. The statement claims that if $n$ is a prime number, then $2n + 1$ will also be a prime number. 2. To test this, let's use an example with $n = 5$, which is a prime number.

1. The given sequence is 2, 3, 5, 7, 11, 13,... 2. This sequence consists of prime numbers: numbers greater than 1 that have no positive divisors other than 1 and themselves.

1. The problem asks for the smallest integer \(n\) such that \(2250n\) is a perfect cube. 2. First, factorize 2250 into its prime factors.

1. The problem is to list prime numbers, which are numbers greater than 1 that have no positive divisors other than 1 and themselves. 2. The first few prime numbers are:

1. The term H.C.F stands for Highest Common Factor, which is the greatest number that divides two or more numbers without leaving a remainder. 2. To find the H.C.F of given numbers

1. The problem is to convert the decimal number 14 into its binary (base 2) equivalent. 2. To convert from decimal to binary, repeatedly divide the number by 2 and record the remai

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