(Predicate Logic) ∀x ∈ N(x > 1 → ∃k ∈ N∃m ∈ N(m ≡ 1(mod 2) ∧ x = 2^k⋅m))
34154
Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
139155
What does 2 to the power x mean in set theory
50266
In the following figure prove that: $AK||BC$
130093
Prove by Induction : $n < 2^n$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
154459
Constructing a HoTT proof term of 1≠0
85770
What is the difference between ∀x(p(x) →q(x)) and ∀x(p(x) ∧q(x))?
157924
$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$
142168
can we a prove ⊢ (α → α) → (α → α)
87928
Proof of logical equivalence of biconditional and other proposition
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$