For $5$ distinct integers $a_i$, $1\le i\le5$, $f(a_i)=2$. Find an integer b (if it exists) such that f(b) = $9$.
35478
Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
45602
Show that is $\int_A f$ exists, then so does $\int_A |f|$
61640
Prove c exists for f:[0,1] -> R
139350
Given two coprime integers, find multiples of them that differ by 1
37219
Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
44745
How many positive integers less than 1000 have distinct digits and are even?
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
100336
Find an integer having the remainders $2,3,4,5$ when divided by $3,4,5,6$, respectively.
157186
Finding integers satisfying $m^2 - n^2 = 1111$
103545
Prove "casting out nines" of an integer is equivalent to that integer modulo 9
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
149071
Let $d$ be any positive integer not equal to $2, 5,$ or $ 13$ , then $\exists a, b \in \{2, 5, 13, d\}$ such that $ab − 1$ is not a perfect square?
66960
Find a polynomial f(x) of degree 5 such that 2 properties hold.
44528
The only natural number $x$ for which $x+\sqrt{-2}$ is a cube in $\mathbb{Z}[\sqrt{-2}]$ is $x=5$
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer