We prove that the theory IΔ0, extended by a weak version of the Δ0-Pigeonhole Principle, proves that every integer is the sum of four squares (Lagrange's theorem). Since the required weak version is derivable from the theory IΔ0 + ∀x (xlog(x) exists), our results give a positive answer to a question of Macintyre (1986). In the rest of the paper we consider the number-theoretical consequences of a new combinatorial principle, the ‘Δ0-Equipartition Principle’ (Δ0EQ). In particular we give a new proof, which can be formalized in IΔ0 + Δ0EQ, of the fact that every prime of the form 4n + 1 is the sum of two squares.
Autori interni: | |
Autori: | BERARDUCCI A; INTRIGILA B |
Titolo: | Combinatorial principles in elementary number theory |
Anno del prodotto: | 1991 |
Digital Object Identifier (DOI): | 10.1016/0168-0072(91)90096-5 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.