New user? Sign up

Existing user? Log in

A container of water and a pump weigh 100 kg at rest. Then, the pump is switched on and sucks the water to \(\SI{1}{\meter}\) high, releasing it back ...

If \(A\neq B\) and \( A^n + B^n \) is an integer for all positive integers \(n,\) must \(A\) and \(B\) both be integers?

If \(A\neq B\) and \( A^n - B^n \) is an integer for all positive integers \(n,\) must \(A\) and \(B\) both be integers?

True or False?

For positive integers \(k \geq 2,\)

\[ \LARGE \left( 2 ^ { 2 ^ k } \right) ^ { \left( 2 ^ { 2 ^ k } \right) } = 2 ^ { 2 ^ { ( k + 2^k ) } } \]

Inspiration

If \( A^2 + B^2\), \(AB\), and \(A + B \) are all integers, must \(A\) and \(B\) both be integers?

Problem Loading...

Note Loading...

Set Loading...