Non inductive proof for square of odd integers
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
92057
Prove that for every odd integer n, there is a group...
125604
Proof that $\mathbb{Z}$ has no zero divisors
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
140841
Induction proof of lower bound for $\sum \sqrt n$
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
4105
Irreducible but not prime in $\mathbb{Z}[\sqrt{-5}] $
121469
Proof of observations on natural numbers being expressed as differences of squares.
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
90076
Prove that every positive integer $n$ is a unique product of a square and a squarefree number
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
104349
Proof by induction involving symmetric groups
143113
Non-inductive, not combinatorial proof of $\sum_{i \mathop = 0}^n \binom n i^2 = \binom {2 n} n$