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John Marty's user avatar
John Marty's user avatar
John Marty's user avatar
John Marty
  • Member for 11 years
  • Last seen more than 8 years ago
47 votes
3 answers
13k views

Find all real numbers $x$ for which $\frac{8^x+27^x}{12^x+18^x}=\frac76$

21 votes
4 answers
1k views

Do there exist infinitely many pairs of primes $(p,q)$ such that $pq$ divides $2^{p-1}+2^{q-1}-2$?

15 votes
5 answers
631 views

Given $a>b>2$ both positive integers, which of $a^b$ and $b^a$ is larger?

14 votes
1 answer
1k views

Show that $4mn-m-n$ can never be a square

12 votes
1 answer
863 views

Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$

9 votes
1 answer
227 views

Elementary Number Theory; prove existence

8 votes
2 answers
276 views

Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$

8 votes
3 answers
403 views

Number theory: Prime powers and cubes

8 votes
1 answer
314 views

Functional Equation - Am I right?

8 votes
3 answers
3k views

Prove that $n^7+7$ can never be a perfect square.

8 votes
1 answer
106 views

Massive expression mod $2^{2013}$

7 votes
2 answers
4k views

Super hard Euclidean Geometry

7 votes
4 answers
379 views

Finding the number of triples $(a,b,c)$ with $-47 \leq a,b,c \leq 47$ and $a+b+c >0$

7 votes
2 answers
727 views

Find the greatest integer $k$ for which $1991^k$ divides $1990^{{1991}^{1992}}+1992^{{1991}^{1990}}$

6 votes
1 answer
148 views

If an integer $n$ is such that $7n$ is the form $a^2 + 3b^2$, prove that $n$ is also of that form.

6 votes
2 answers
443 views

Can both $x^2 + y+2$ and $y^2+4x$ be squares?

6 votes
1 answer
318 views

What happens to the infinite monkey theorem when there are an infinite number of keys on the typewriter?

6 votes
1 answer
1k views

Functional Equation $f(f(n))=3n$ [duplicate]

6 votes
2 answers
2k views

For every positive integer n, the number $a^{2^n}−1$ has at least n+1 distinct prime divisors

6 votes
4 answers
4k views

Euclidean Geometry: Diagonals of Cyclic Hexagon

6 votes
3 answers
844 views

Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$

6 votes
4 answers
294 views

Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$

5 votes
1 answer
104 views

How to prove that all primes $p$ will have a power $p^k$ with a $2$ in its decimal representation?

5 votes
2 answers
415 views

Algebra question from Australia national olympiad 2013

5 votes
2 answers
156 views

Finding all $f:\mathbb{R} \rightarrow \mathbb{R}$ s.t $f(x^2+f(y))=(x-y)^2f(x+y)$ [duplicate]

5 votes
1 answer
135 views

Why are these three lines concurrent?

5 votes
1 answer
66 views

Question on inequalities of symmetric means.

5 votes
2 answers
169 views

Showing $\{x\} + \{\frac{1}{x}\} \lt 1.5$ and other problems.

4 votes
2 answers
927 views

Euclidean Geometry Area Problem

4 votes
2 answers
456 views

For what $n$ and $m$ is this number a perfect square?