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Hamid Reza Ebrahimi
  • Member for 7 years
  • Last seen more than 1 year ago
10 votes
2 answers
576 views

Show that among any consecutive $16$ natural numbers one is coprime to all others

9 votes
3 answers
183 views

For function $f:[0,1]\rightarrow \Bbb R$ we know : $f(x+y)\geq f(x)+f(y)$.Prove that $f(x)\leq 2x$

9 votes
1 answer
189 views

Verify surjectivity of the function $f$ satisfying: $f(x)+f(x^2)=x$

7 votes
3 answers
396 views

Find all positive integers satisfying: $x^5+y^6=z^7$

6 votes
2 answers
191 views

What's $\alpha+\beta$ if we have: $\alpha^3-6\alpha^2+13\alpha=1$ and $\beta^3-6\beta^2+13\beta=19$ ($\alpha$ and $\beta$ are Real)

6 votes
1 answer
641 views

Find all polynomials with real coefficients $P(x),Q(x)$ such that for every real number $x$ we have: $P(Q(x))=P(x)^{2017}$

5 votes
1 answer
238 views

Find all positive integers $k,m,n$ satisfying: $\frac1k+\frac1m+\frac1n=\frac{1}{1996}$

5 votes
6 answers
1k views

Solve the following nonlinear system of equations:$ xy+xz+yz=12 , xyz=2+x+y+z$

5 votes
3 answers
110 views

Show that $1^7+7^7+13^7+19^7+23^7\equiv{0}\pmod{63}$

5 votes
5 answers
1k views

Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$

5 votes
2 answers
572 views

"Good" subsets of natural numbers

5 votes
6 answers
450 views

Find the rightmost digit of: $1^n+2^n+3^n+4^n+5^n+6^n+7^n+8^n+9^n$

5 votes
2 answers
196 views

Find $I$ in $\frac{\overline{SIX}}{\overline{NINE}}=\frac23$

4 votes
5 answers
2k views

Find all positive integers $n$ such that $n^2+n+43$ becomes a perfect square

4 votes
3 answers
878 views

Show that among every consecutive 5 integers one is coprime to the others

4 votes
4 answers
1k views

Perfect square product among 17 integers

4 votes
5 answers
168 views

Find minimum of $a+b+c+\frac1a+\frac1b+\frac1c$ given that: $a+b+c\le \frac32$

3 votes
2 answers
152 views

Find all positive integers such that: $n^2-3|3n^3-5n^2+7$

3 votes
2 answers
64 views

Find the maximum of positive integer $k$ so that for all positive real numbers $x$ we have: $x^6+x^5+x^4+x^2+x+4>kx^3$

3 votes
2 answers
103 views

In the following figure prove that $AE||EF$ (without using similar triangles)...

3 votes
2 answers
113 views

Find sum of all positive real numbers $x$ such that $\sqrt[3]{2+x} + \sqrt[3]{2-x}$ becomes an integer.

3 votes
1 answer
488 views

Among any $11$ integers, sum of $6$ of them is divisible by $6$

3 votes
3 answers
958 views

How many ways are there to go through all intersections and come back to starting point in the following street map...

3 votes
5 answers
2k views

Calculate the area of center square in the following figure [duplicate]

3 votes
2 answers
367 views

Show that if $ \gcd(a,b)=d,\gcd(a,c)=f,\gcd(b,c)=1 \ \Rightarrow\gcd(a,bc)=df$

3 votes
2 answers
150 views

Show that :$89|2^{44}-1$ [duplicate]

3 votes
1 answer
93 views

Inequality in a triangle: $BC > \frac 12AB$ if $∠A > ∠B$ (self-answered)

3 votes
4 answers
154 views

Minimum number of fractions to be summed up to $\frac45$

3 votes
7 answers
206 views

Find all positive integer roots of $\,5xy=19x+96y$

3 votes
2 answers
187 views

Upper bound for $\gcd(a,b)$ if $\frac{a+1}{b}+\frac{b+1}{a}\in\Bbb{N}$

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