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Sunaina Pati's user avatar
Sunaina Pati's user avatar
Sunaina Pati's user avatar
Sunaina Pati
  • Member for 3 years, 11 months
  • Last seen more than a month ago
17 votes
3 answers
11k views

Book recommendation : Olympiad Combinatorics book

9 votes
6 answers
3k views

Four Number Theorem: any two factorizations $\,ab = cd\,$ have a common refinement

9 votes
1 answer
455 views

Conjecturing when $M$ is good

9 votes
4 answers
670 views

Solutions to $2^a3^b+1=2^c+3^d$

8 votes
2 answers
238 views

why $\left(\left( \left(-\frac{1}{4}\right)^{-2}\right)^\frac{1}{4}\right) \neq \left(\left(-\frac{1}{4}\right)^{-\frac{1}{2}}\right)$?

8 votes
4 answers
806 views

USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$

7 votes
1 answer
286 views

Prove that if lines $FP$ and $GQ$ intersect at $M$, then $\angle MAC = 90^\circ$.

7 votes
2 answers
347 views

Solve over the positive integers: $7^x+18=19^y.$

7 votes
2 answers
272 views

Solve the generalised diophantine equation: $x_1^2 + x_2^2 + \dots + x_n^2 = kx_1 x_2\dots x_n$

6 votes
2 answers
274 views

Generalisation of IMO 1990/P3:For which $b $ do there exist infinitely many positive integers $n$ such that $n^2$ divides $b^n+1$?

6 votes
5 answers
325 views

CGMO 2020: Prove that $X, P, Q, Y$ are concyclic.

6 votes
1 answer
117 views

Let $AD\cap (BFC) $ in points $P$ and $Q$ and let $AD\cap (ABE)=M$ then $MP=MQ$.

6 votes
2 answers
218 views

Prove that $P=RA'\cap EF$, then $DP\perp EF$.

6 votes
3 answers
257 views

Find odd primes $p$ and $q$ such that $(p-1)\mid {3q-1}$ and $(q-1)\mid{3p-1}$.

5 votes
1 answer
307 views

Prove that $N,R,F$ are collinear

5 votes
1 answer
187 views

USATST 2018/P4 : Prove that $OA\perp RA$ [Proof Verification needed]

5 votes
1 answer
129 views

Show that $\angle BOC=\angle AOD$.

5 votes
1 answer
998 views

ELMO 2019/G3: Prove that if $GH$ and $EF$ meet at $T$, then $DT\perp EF$.

5 votes
1 answer
272 views

USAJMO 2017 P4: triples $(a,b,c)$ such that $(a-2)(b-2)(c-2)+12$ is a prime number that divides the positive number $a^2+b^2+c^2+abc-2017$?

5 votes
1 answer
175 views

What is the maximum number of consecutive sides whose lengths you can choose without uniquely determining the polygon?

5 votes
1 answer
100 views

Prove that there exists an integer $a$ with $1 \leq a \leq p-2$ such that neither $a^{p-1}-1$ nor $(a+1)^{p-1}-1$ is divisible by $p^2$.

5 votes
1 answer
144 views

Triangle table: Moscow MO 1958 triangular table with numbers

5 votes
3 answers
908 views

Prove that ${2p\choose p}\equiv 2\pmod {p^2}.$

4 votes
1 answer
459 views

Prove that a prime $p\equiv 1 \pmod 8$ can be written in the form $x^2+2y^2.$

4 votes
2 answers
161 views

Compute $\frac 17$ in $\Bbb{Z}_3$

4 votes
2 answers
254 views

Prove that the infinite $\sum_{\text{ p prime}}\frac{1}{2^p}$ is an irrational number. [duplicate]

4 votes
0 answers
132 views

Proof Verification: Find all positive integer $n$ for which $n^2|2^n+1.$ [duplicate]

4 votes
1 answer
103 views

Prove that $s_p(n-1)+s_p(n)+1-s_p(2n)\ge v_p(n)\cdot (p-1)$ for $p|n$

4 votes
3 answers
263 views

Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP

4 votes
1 answer
215 views

Show that $A-$excircle is tangent to $(AST)$