Problem #PRU-100330

Problems Number Theory Arithmetic operations. Number identities Divisibility Odd and even numbers

Problem

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?

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