Newbetuts

What are statements about the natural numbers where induction is impossible or unnecessary to prove?

Let g: $\mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z}$ be given by: $g(x,y) = (x+y, x-y)$

Strong induction $n=2^a\cdot b$ [duplicate]

"Let" in math texts

If $b_nb_{n-1} \cdots b_0$ is the binary representation of natural $x$, and if $(b_0-b_1+b_2-b_3+\cdots+(-1)^nb_n)=0\pmod3$, then $x=0\pmod3$

Proof that there are infinitely many positive rational numbers smaller than any given positive rational number.

Is the following generalization of Cauchy-Schwarz inequality true?

are two consecutive numbers relatively prime?

Proof variance of Geometric Distribution

Primitive root mod $2p^k$.

Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence

Proof verification in multi-variable calculus using $\epsilon-\delta$ statement

the space of continuous functions is complete

Big O notation sum rule

Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$ [duplicate]

Is it legitimate to specify a statement as a Theorem if it is proved using numerical methods (since it can't be proved analytically)?

Four variables inequality proof [closed]

My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

New posts in proof-writing

What are statements about the natural numbers where induction is impossible or unnecessary to prove?

Find the Roots of $(x+1)(x+3)(x+5)(x+7) + 15 = 0$

Are there infinitely many primes of form $\underbrace{3\dots3}_n{}1$?

Let g: $\mathbb{Z} \times \mathbb{Z} \rightarrow \mathbb{Z} \times \mathbb{Z}$ be given by: $g(x,y) = (x+y, x-y)$

Strong induction $n=2^a\cdot b$ [duplicate]

"Let" in math texts

If $b_nb_{n-1} \cdots b_0$ is the binary representation of natural $x$, and if $(b_0-b_1+b_2-b_3+\cdots+(-1)^nb_n)=0\pmod3$, then $x=0\pmod3$

Proof that there are infinitely many positive rational numbers smaller than any given positive rational number.

Is the following generalization of Cauchy-Schwarz inequality true?

are two consecutive numbers relatively prime?

Proof variance of Geometric Distribution

Primitive root mod $2p^k$.

Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence

Proof verification in multi-variable calculus using $\epsilon-\delta$ statement

the space of continuous functions is complete

Big O notation sum rule

Prove that $x = 2$ is the unique solution to $3^x + 4^x = 5^x$ where $x \in \mathbb{R}$ [duplicate]

Is it legitimate to specify a statement as a Theorem if it is proved using numerical methods (since it can't be proved analytically)?

Four variables inequality proof [closed]

My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.