Can someone help me prove that $\tau(n)$ is odd iff $n$ is a perfect square.
48787
A number is a perfect square if and only if it has odd number of positive divisors
48430
Prove the following sequence always results in a perfect square.
41641
$(n-7)(n+7)=$ some perfect square
21152
Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized
134121
Determining all the positive integers $n$ such that $n^4+n^3+n^2+n+1$ is a perfect square.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
72511
If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
28781
$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
84220
Questions on perfect squares
120498
Why perfect square has odd number of factors
142724
Prove that for all integers $x$ and $y$, $x - y$ is odd if and only if $x + y$ is odd.
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
103538
Partitions of $n$ into distinct odd and even parts proof
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
130499
How can $p^{q+1}+q^{p+1}$ be a perfect square?
94570
Proof that every odd integer is a difference of two squares
104494
$m$ doesn't come in the sequence $a_n=[n+\sqrt{n}+\frac{1}{2}]$ iff m is a perfect square