My p cents worth:

p is prime iff the only two factors of p are p and p/p provided
p <> p - p and
p <> p/p

Regards
Patrick

[quote=Patrick123;99753]My p cents worth:

p is prime iff the only [B]two[/B] factors of p are p and p/p provided
p <> p - p and
p <> p/p

Regards
Patrick[/quote]Violation.

[QUOTE=Mini-Geek;99756]Violation.[/QUOTE]

Whoops let's rephrase that:

p is prime iff its only factors are p and p/p provided
p <> p - p and
p <> p/p and
p is positive.

Regards
Patrick

[QUOTE=R.D. Silverman;99523]An integer p is prime if and only if for all A,B, such that A^2 = B^2 mod p,
then A=B mod p or A=-B mod p.[/QUOTE]

So, 1 and 6 are primes then?

[QUOTE=Jushi;99870]So, 1 and 6 are primes then?[/QUOTE]How do you define an equality modulo 1 ?

[QUOTE=S485122;99874]How do you define an equality modulo 1 ?[/QUOTE]

Usually, "a = b mod c" means "c divides (b-a)". Then any two integers are equal mod 1, because 1 divides any integer.

[quote=S485122;99874]How do you define an equality modulo 1 ?[/quote]
That's not much worse than equality mod [tex]2\pi[/tex] which everyone knows from study of trigonometric functions... "x = y (mod z)" is defined for any number z (including 0, where it gives equality) as he wrotes, or [tex]x-y \in z\,\mathbb Z[/tex] where Z are the integers, i.e. zZ are all numbers of the form zk with k some integer.