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Davood's user avatar
Davood's user avatar
Davood
  • Member for 6 years, 4 months
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21 votes

Solving an infinite product of consecutive square roots

15 votes

Proving that $\{x\in\Bbb{R}\mid 1+x+x^2 = 0\} = \varnothing$ without the quadratic formula and without calculus

13 votes
Accepted

Example of an integral domain which is not a field

13 votes
Accepted

When is this integer a perfect square: $n^2 + 20n + 12$

12 votes
Accepted

Finding the minimum value of $a^2+b^2+c^2$

9 votes
Accepted

Can every number $n$ be written as the sum of $n$ different prime numbers?

8 votes

Can sum of a rational number and its reciprocal be an integer?

8 votes

Sequence : $f(f(n))+f(n+1)=2n$

7 votes
Accepted

Show that for any integer $n\ge 6$, the inequality $2^n>7n$ holds.

6 votes

Finding integer solutions to $y^2=x^3-2$

5 votes
Accepted

Determine all pairs $(a,b)$ of positive integers such that $ab^2+b+7$ divides $a^2b+a+b$

5 votes
Accepted

Proof that the sum of the even side and the hypotenuse of a coprime (and positive) Pythagorean triple is a square number

5 votes
Accepted

Prove that a group $G$ is Abelian if and only if $(ab)^{-1}=a^{-1}b^{-1}$

5 votes

Example of a power of 3 which is close to a power of 2 (Related to music theory and Superparticular ratios)

4 votes
Accepted

Invertible matrices multiplication

4 votes
Accepted

How can I show $q^k$ does not divide ${{n}\choose{q}}$ when $q$ is a prime factor of $n$ and $k$ is the largest integer such that $q^k$ divides $n$?

4 votes

Is there a prime $p$ whose successor is greater than $2p$?

4 votes
Accepted

Any integer is of the form $n=a_1^2+a_2^2+a_3^2-a_4^2-a_5^2$

4 votes

$x^2 + 3x + \frac{3}x + \frac{1}{x^2} = 26$ and $x$ can be written as $a + \sqrt{b}$ where $a$ and $b$ are positive integers, then find $a + b$.

4 votes
Accepted

Euler's theorem and $Z_p^*$

4 votes
Accepted

Find all solutions of $9^x-4^y=5^z$ over the naturals

4 votes

Prove that if $\gcd(a,b) = 1$, then $\gcd(ab,a^2+b^2)=1.$

4 votes
Accepted

Prove or disprove : If $a\equiv b$ mod $m$, when $a,b,m\in \mathbb{Z}$ , then $a^3\equiv b^3$ mod $m^2$.

3 votes

Find $(a^2+b^2),$ where $(a+b)=\dfrac{a}{b}+\dfrac{b}{a}$

3 votes

Perfect Squares: relatively prime and increasing arithmetic progression

3 votes
Accepted

Prove that if $2^{m+1}+1$ divides $3^{2^m}+1$, then $2^{m+1}+1$ is a prime

3 votes
Accepted

How to prove that $\sum_{i=0}^n\binom{n}{i}^2 =\binom{2n}{n}$

3 votes
Accepted

Prove that, there are infinitly many integers $n$; such that $n\mid 2^n+1$.

3 votes
Accepted

Prove of infinite ways of writing $n$ as $\pm 1^2\pm 2^2\pm....\pm k^2$

3 votes
Accepted

If $N$ is the integer $2^43^35^27$ find the smallest positive integer $m$ such that $x^m \equiv 1 \mod N$ for all integers coprime to $N$