Prove that $n=a^2+b^2-c^2$.
140140
An identity which applies to all of the natural numbers
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
66387
Prove $(x_1+.....+x_n)^2 \leq n(x_1^2 + .....+x_n^2)$
85731
Prove by induction that $n! > n^2$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
14480
Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
55266
Prove that $(n+1)^{n-1}<n^n$
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
44309
Prove $5a^2 ≠ 3b^2$ for all non-zero rational numbers $a$ and $b$
31104
$a+b+c =0$; $a^2+b^2+c^2=1$. Prove that: $a^2 b^2 c^2 \le \frac{1}{54}$
118507
Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$