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John Omielan

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33
Finding the number of digits of a given integer.
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11
It is impossible for $(x-1)^2+x^2+(x+1)^2$ to be a perfect square
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11
Max product of $20$ numbers with mean $12$ if $n$-th number is $\frac{n}2$ or $2n$?
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9
Is $f(x) = |x|^{3/2}$ differentiable at $0$?
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8
Prove that the product of any two numbers between two consecutive squares is never a perfect square
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8
4 distinct integers with prime sum for each triple
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8
Are the functions $\sin^2(x)$ and $\cos^2(x)$ linearly independent? $a\sin^2(x)+b\cos^2(x)=0$, such that the domain is the set $~\{0\}~$
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8
Difference between strictly increasing and increasing functions
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7
Show that $\lim\limits_{(x,y)\to(0,0)}[x\sin(1/y) + y\sin(1/x)]$ exist
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6
Prove $\sin(a) < a < \tan(a)$ when $0 < a < \pi/2$
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6
Why is the sqrt of a matrix different to ^0.5
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6
Show that $\frac{f(x)}{x}$ is a decreasing function implies that $f(x)$ is subadditive
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6
How can I simplify $(4ab^{-1})^{-2}$
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6
exist infinitely many positive integers $n$ such $\omega (n)+\omega (n+1)\equiv 0\pmod 3$
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6
Show that $x^5+x+1=0$ has a solution in $\mathbb{R}$
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6
Sixth grade math (number related) problem
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6
How is the missing digit calculated?
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6
For any positive integer $n>3$, there exists at least $1$ integer $k$ such that $n+k$ and $n-k$ are primes.
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5
If $\sum a_{n}$ is a series of positive terms and $b_{n} = (a_{1}+a_{2}+a_{3}+ \dots +a_{n})/n$ then $\sum b_{n}$ is divergent. (True/false)
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5
Find the limit of $e^x/2^x$ as $x$ approaches infinity
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5
Positive integer solution of Diophantine equation $a^2+b^2=z^3$
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5
Arrange $n$ tiles in a rectangle pattern
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5
Proof that $x^{(n+4)} \bmod 10 = x^n \bmod 10\,$ for $\,n\ge 1$
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5
If $f(4xy)=2y[f(x+y)+f(x-y)]$ and $f(5)=3$, find $f(2015)$
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5
Prove that $\gcd(2^n + 7^n, 2^n - 7^n) = 1$
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5
Fair gambler's ruin problem intuition
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5
Can $p(x)q(x+1)$ and $q(x)p(x+1)$ be the same?
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5
Prove that there is $n\in\mathbb{N}$ such that $n!$ starts with 1996
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5
Prove that if $x$ is odd, then $x^2$ is odd
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5
How to prove $f(x)=x\cos(x)$ is a many to one function?
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