New user? Sign up

Existing user? Sign in

Find the smallest integer \(n\) greater than 100 such that the fraction \(\dfrac { 9n+5 }{ 10n+3 } \) will be reducible.

\[a_{2016}x^{2016} + a_{2015}x^{2015} + \cdots + a_1x + a_0= 0\]

The coefficients of the equation above are independently sampled from a uniform distribution over \([0,1],\) and the ...

Let \(f(n)\) be a function defined on the non-negative integers given the following facts:

\(f(0)=f(1)=0 \).

\( f(2)=1 \)

For \(n>2\), \(f(n)\) gives the smallest ...

\[ \begin{cases} x + y + z + 18a + b = 135802458 \\ x + y + 18z + a + b = 135802458\\ 18x + y + z + a + b = 135802458\\ x + 18y + z + a + b = 135802458\\ x + y + z + a + 18b = 135802458 \end{cases} \]

Consider this equation

\[2^x=x^2\]

There are 2 trivial solutions, namely \(x=2\) and \(x=4\)

However, the equation is known to also have a negative solution. Find ...

Problem Loading...

Note Loading...

Set Loading...