Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5
11359
Determine the Set of a Sum of Numbers
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
70311
Trying to prove (A ∩ B) − C = (A − C) ∩ (B − C)
130093
Prove by Induction : $n < 2^n$
87665
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
57418
How to prove this statement: $\binom{r}{r}+\binom{r+1}{r}+\cdots+\binom{n}{r}=\binom{n+1}{r+1}$
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
49440
Prove that the interval $ \ [0,2)$ and $ \ [5,6) \cup [7,8)$ have the same cardinality
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
149758
How to prove $\log n < n$?
93964
Proving that $f$ is a bijection from $N$x$N$ to $N$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
71451
A proof by strong induction that $a_n\le3^n$ where $a_n=a_{n-1}+a_{n-2}+a_{n-3}$
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.