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Prove that $2018^{2019}> 2019^{2018}$ without induction, without Newton's binomial formula and without Calculus.
number-theory
inequality
alternative-proof
Alternative proof of $\sqrt{2}$ is irrational assistance.
proof-verification
alternative-proof
Fascinating induction problem with numerous interpretations
geometry
induction
recreational-mathematics
alternative-proof
What is the relation between 'the order of $x^k = n/{\gcd(k,n)}$' and Lagrange's Theorem?
abstract-algebra
group-theory
elementary-number-theory
alternative-proof
cyclic-groups
Is there some elementary proof of invariance of domain?
general-topology
alternative-proof
How to prove this algebraic version of the sine law?
algebra-precalculus
trigonometry
systems-of-equations
alternative-proof
Is there an easy way to see that this simple recurrence is 9-periodic? [duplicate]
recurrence-relations
dynamical-systems
absolute-value
alternative-proof
How is Leibniz's rule for the derivative of a product related to the binomial formula? [duplicate]
calculus
combinatorics
intuition
alternative-proof
Proving that $\sqrt{2}$ is irrational with a math level of a middle school student?
alternative-proof
irrational-numbers
Diagonals of quadrilateral $ABCD$ intersect at $E$. Given $\frac{AE}{AC} = λ,\>\frac{BE}{BD} = μ$. Find ratios for sides
geometry
proof-writing
alternative-proof
A trivial proof of Bertrand's postulate
elementary-number-theory
alternative-proof
solution-verification
prime-gaps
Use $\delta-\epsilon$ to show that $\lim_{n\to\infty} a^{\frac{1}{n}} = 1$?
real-analysis
limits
alternative-proof
epsilon-delta
Exercise 6, Section 17 of Munkres’ Topology
general-topology
proof-writing
solution-verification
alternative-proof
Prove that $x-1$ is a factor of $x^n-1$
abstract-algebra
polynomials
alternative-proof
Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$
integration
definite-integrals
contour-integration
closed-form
alternative-proof
Is this proof that $\sqrt 2$ is irrational correct?
irrational-numbers
alternative-proof
Proof that a certain entire function is a polynomial
complex-analysis
analysis
alternative-proof
How to show that $\lfloor n/1\rfloor+\lfloor n/2 \rfloor+....+\lfloor n/n\rfloor+\lfloor{\sqrt{n}}\rfloor$ is even?
elementary-number-theory
alternative-proof
Exercise 9, Section 17 of Munkres’ Topology [duplicate]
general-topology
proof-writing
solution-verification
alternative-proof
Does Nakayama Lemma imply Cayley-Hamilton Theorem?
linear-algebra
abstract-algebra
commutative-algebra
modules
alternative-proof
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