Find maximum n such that $2^n$ divides $2559^{2^{13}}-2557^{2^{13}}$
2026-04-03 01:51:37.1775181097
divisible problem
74 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ELEMENTARY-NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- How do I show that if $\boldsymbol{a_1 a_2 a_3\cdots a_n \mid k}$ then each variable divides $\boldsymbol k $?
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- Algebra Proof including relative primes.
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
- algebraic integers of $x^4 -10x^2 +1$
- What exactly is the definition of Carmichael numbers?
- Number of divisors 888,888.
Related Questions in CONTEST-MATH
- Solution to a hard inequality
- Length of Shadow from a lamp?
- All possible values of coordinate k such that triangle ABC is a right triangle?
- Prove that $1+{1\over 1+{1\over 1+{1\over 1+{1\over 1+...}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+...}}}}$
- Lack of clarity over modular arithmetic notation
- if $n\nmid 2^n+1, n|2^{2^n+1}+1$ show that the $3^k\cdot p$ is good postive integers numbers
- How to prove infinitely many integer triples $x,y,z$ such that $x^2 + y^2 + z^2$ is divisible by $(x + y +z)$
- Proving that $b-a\ge \pi $
- Volume of sphere split into eight sections?
- Largest Cube that fits the space between two Spheres?
Related Questions in DIVISIBILITY
- Reciprocal-totient function, in term of the totient function?
- Can we find integers $x$ and $y$ such that $f,g,h$ are strictely positive integers
- Positive Integer values of a fraction
- Reciprocal divisibility of equally valued polynomials over a field
- Which sets of base 10 digits have the property that, for every $n$, there is a $n$-digit number made up of these digits that is divisible by $5^n$?
- For which natural numbers are $\phi(n)=2$?
- Interesting property about finite products of $111..1$'s
- Turn polynomial into another form by using synthetic division
- Fractions of the form $\frac{a}{k}\cdot\frac{b}{k}\cdot\frac{c}{k}\cdots=\frac{n}{k}$
- Proof: If $7\mid 4a$, then $7\mid a$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
By using Lifting the Exponent, we know that: $$n=v_2({2559}^{2^{13}}-{2557}^{2^{13}})=v_2(2559-2557)+v_2(2^{13})+v_2(2559+2557)-1\\=v_2(2)+13+v_2(5116)-1=1+13+2-1=15$$