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818
Membership
Stats
Questions
253
Réponses
98
256 Questions
127 Answers
-2
97
1
+818
quick question
In a right triangle, one of the angles is $45^\circ,$ and the hypotenuse is $6$ inches. Find the area of the triangle in square inche
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maximum
15 août 2023
-2
52
2
+818
need help
Can anyone give a hint here?
Given a positive integer $n,$ prove that there exists a positive integer $m > 1000$ such that $m \equiv 7 \pmod{n}$ and $\gcd(m,n) = 1.$
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maximum
15 août 2023
-1
101
1
+818
hard number theory congruence
does anybody have any ideas?
The prime $p$ has the property that the congruence $$n^2 \equiv -1\pmod{p}$$ has no solutions $n$. Determine the sum of all such primes $p$.
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maximum
14 août 2023
-2
45
2
+818
help with squares
help I have question about squares
Let $a$ and $b$ be non-zero integers. If both $a^2$ and $b^2$ have at most three digits, then what is the greatest possible difference between $a^2$ and $b^2?$
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maximum
14 août 2023
-2
55
2
+818
pythagorean theorem
The hypotenuse of right triangle $ABC$ is $AB$. The area of square $BCDE$ is $144$. If $AB$ and $AC$ are each integers less than $20$, how many possibilities are there for their lengths?
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maximum
14 août 2023
-2
88
1
+818
functions
Help me plz
For integers $n$, let \[f(n) = \left\{
\begin{array}{cl}
n & \text{ if }n\text{ is odd}, \\
n -1 & \text{ if }n\text{ is even}.
\end{array}<#> \right.\] Find $f(f(f(f(f(4)))))$.
lire plus ..
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maximum
14 août 2023
-2
61
1
+818
piecewise functions
Let \[f(x) =
\begin{cases}
x^2&\text{if } x\le 3, \\
3ax &\text{if } x>3.
\end{cases}<#> \]<#> Find the value of $a$ if the graph of $y=f(x)$ is continuous (which means the graph can be drawn without lifting your
lire plus ..
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maximum
14 août 2023
-1
104
3
+818
plz help with digit
I need help with this
Find the number of times the digit $9$ appears in the list of all integers from $1$ to $150$. (The number $ 99 $, for example, is counted twice, because $9$ appears two times in it.)
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maximum
14 août 2023
-1
55
1
+818
congruence
What is the smallest positive integer $n$ such that $3n \equiv 1356 \pmod{5}?$
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maximum
14 août 2023
-1
60
0
+818
polynomial roots
Find all real numbers $a$ such that the roots of the polynomial
\[x^3 - 12x^2 + 73x + a\]
form an arithmetic progression and are not all real.
maximum
13 août 2023
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24
23
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5
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3
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1
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#1
+818
-1
Do not post AoPS homework.
maximum
20 janv. 2025
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11
10
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2
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