Newbetuts

Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square

What is this pattern found in the first occurrence of each $k \in \{0,1,2,3,4,5,6,7,8,9\}$ in the values of $f(n)=\sqrt{n}-\lfloor \sqrt{n} \rfloor$?

Numbers that are clearly NOT a Square

What is the ratio of prime numbers to perfect squares

If a and b are relatively prime and ab is a square, then a and b are squares.

When is $2^n -7$ a perfect square?

Math olympiad 1988 problem 6: canonical solution (2) without Vieta jumping

A number is a perfect square if and only if it has odd number of positive divisors

Is $100$ the only square number of the form $a^b+b^a$?

Why is there a pattern to the last digits of square numbers?

How to compute 2-adic square roots?

If $n$ is an odd natural number, then $8$ divides $n^{2}-1$

Is difference of two consecutive sums of consecutive integers (of the same length) always square?

Can a number be equal to the sum of the squares of its prime divisors?

The sum of the first $n$ squares is a square: a system of two Pell-type-equations

New posts in square-numbers

Show that every $n$ can be written uniquely in the form $n = ab$, with $a$ square-free and $b$ a perfect square

How to explain to a 14-year-old that $\sqrt{(-3)^2}$ isn't $-3$?

Why are the last two digits of a perfect square never both odd?

Find All $x$ values where $f(x)$ is Perfect Square

Square Fibonacci numbers

Prove that the square root of a positive integer is either an integer or irrational

What is this pattern found in the first occurrence of each $k \in \{0,1,2,3,4,5,6,7,8,9\}$ in the values of $f(n)=\sqrt{n}-\lfloor \sqrt{n} \rfloor$?

Numbers that are clearly NOT a Square

What is the ratio of prime numbers to perfect squares

If a and b are relatively prime and ab is a square, then a and b are squares.

When is $2^n -7$ a perfect square?

Math olympiad 1988 problem 6: canonical solution (2) without Vieta jumping

A number is a perfect square if and only if it has odd number of positive divisors

Is $100$ the only square number of the form $a^b+b^a$?

Why is there a pattern to the last digits of square numbers?

How to compute 2-adic square roots?

If $n$ is an odd natural number, then $8$ divides $n^{2}-1$

Is difference of two consecutive sums of consecutive integers (of the same length) always square?

Can a number be equal to the sum of the squares of its prime divisors?

The sum of the first $n$ squares is a square: a system of two Pell-type-equations