Theorem 5.11. The incidence graph In (q) is a Cayley graph. Exercise 5.12. Let q be, as usual, a power of a prime. Show
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- Theorem 5 11 The Incidence Graph In Q Is A Cayley Graph Exercise 5 12 Let Q Be As Usual A Power Of A Prime Show 1 (9.94 KiB) Viewed 29 times
- Theorem 5 11 The Incidence Graph In Q Is A Cayley Graph Exercise 5 12 Let Q Be As Usual A Power Of A Prime Show 2 (21.52 KiB) Viewed 29 times
Exercise 5.12. Let q be, as usual, a power of a prime. Show that there are q + 1 numbers among {1,2,..., q² +q+1} with the following property: if someone picks two different numbers from the list, and tells you their difference, then you know the numbers.
Theorem 6.1. The quadratic signature o is multiplicative on F*, and it is explicitly given by the 'Euler formula' o(a)= a(9-1)/2
Lemma 6.4. Put Je = Σ σ(α)σ(b). a+b=c Then Je-o(-1) if c #0, and Jo = o(-1) (q-1). =