10
A pattern appearing in the powers of $\phi$
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10
Suppose we roll a fair $6$ sided die repeatedly. Find the expected number of rolls required to see $3$ of the same number in succession.
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10
How to approach proofs similar to "Show a group, $G$, is infinite if $G = \langle r, s, t\mid rst = 1\rangle $"
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10
Prove that $2^n$ does not divide $n!$
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10
Probability of selecting an even number from the set of natural numbers
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10
Is there a number such that the sum of its digits is 10 and the sum of the digits of the number squared is 100?
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10
If $f(x)+g'(x)=g(x)+f'(x)$ is there any way to find what "$f(x)$" could be (without having $f'(x)$)?
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10
Your friend has given you his list of 115 best Doctor Who episodes in order of greatness
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10
If $p$ is prime then $2p+1$ cannot be square
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10
Squaring is not an injective operation so why is it allowed?
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10
Integer function which takes every value infinitely often
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10
Does every prime of the form $4k+1$ divide a number of the form $4^n+1$?
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10
Prove that there are no natural numbers $x$ whose digits are $0$ or $2$, such that $x$ is a perfect square.
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10
Can you place $15$ integers around a circle such that sum of every $4$ consecutive numbers is either $1 $ or $ 3$?
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10
Why is $e^x$ the only function that is its own derivative?
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10
Besides trivial solution, are there $A$ and $B$ such that $AB=A+B$?
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9
Find all functions satisfying $f(x)f(y)=f(x+y)+xy$
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9
Factoring the polynomial $2X^{10}+4X^5 +3$ into irreducible factors in $(\mathbb{Z} / 5\mathbb{Z})[X].$
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9
What methods can I use to show that $2^{50} < 3^{33}$, without a calculator
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9
The number of divisors being less than or equal to twice the square root of a natural number
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9
Functions satisfying $f(x+y)+x= f(x)f(y)$
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9
Intuitive/Visual solution for: There are $k$ balls in a bowl. How many draws does it on average take, to get one specific ball?
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9
Proving that $3^{n+2}$ does not divide $2^{3^n} +1$ for any positive integer $n$
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9
Functional puzzle: find $f(2)$
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9
Probability of all 3 cards drawn being the same number
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9
Roll a dice infinitely many times, what is the probability of getting a 5 before a 6
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9
100 dresses in a year
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9
Algebraic proof that two statements of the fundamental theorem of algebra are equivalent
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9
Two players throw a die until the sequence $1,2,3$ appears, and the winner is the one who roll $3$. What is the probability the second player wins?
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9
How to construct a sequence that has a subsequence convergent to every $k\in \Bbb{N}$?
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