The Hatter is obsessed with odd numbers. He is very determined to represent 1 as \[1 = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d},\] where \(a\), \(b\), \(c\), and \(d\) are all odd.
Alice is very sceptical about it. Do you think you can help Alice to persuade the Hatter that it is impossible?