Prove that it is impossible to find any positive integers a, b, c such that $(2a+b)(2b+a) = 2^c$
34666
Prove that the expression cannot be a power of 2
150085
Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$
32524
Flawed proof that all positive integers are equal
77547
Find integers $a,b,c,d$ such that
22973
Show that an integer of the form $8k + 7$ cannot be written as the sum of three squares.
23080
Prove that $a^2(b+c-a)+b^2(a+c-b)+c^2(a+b-c) \leq 3abc.$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
134857
Find $(a,b)$ if $x^2-bx+a = 0, x^2-ax+b = 0$ both have distinct positive integers roots
6621
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
135955
Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
119582
How to select the right modulus to prove that there do not exist integers $a$ and $b$ such that $a^2+b^2=1234567$?
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
28099
Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers.
63651
If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.
11868
Let $a,b,c\in \Bbb R^+$ such that $(1+a+b+c)(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=16$. Find $(a+b+c)$