###### Mathematics

## Exercises in Elementary Number Theory (III)

Exercise 1 The Fermat numbers are defined as follows: \[ F_{n} = 2^{2^{n}} + 1 \quad n =0,1,2,\cdots \] Prove that all Fermat numbers with \(n \gt 1 \) have the last digit equal to \(7\). HintThe number \(2^{2^{2}} = 16 \) ends with the digit \(6 \). The same Read more…