Editing Strong pseudoprime (section)

==Formal definition==
An odd composite number ''n'' = ''d'' · 2<sup>''s''</sup> + 1 where ''d'' is odd is called a strong (Fermat) pseudoprime to base ''a'' if:

: <math>a^d\equiv 1\pmod n</math>
or
: <math>a^{d\cdot 2^r}\equiv -1\pmod n\quad\mbox{ for some }0 \leq r < s .</math>

(If a number ''n'' satisfies one of the above conditions and we don't yet know whether it is prime, it is more precise to refer to it as a strong [[probable prime]] to base ''a''. But if we know that ''n'' is not prime, then we may use the term strong pseudoprime.)

The definition is trivially met if {{math|<var>a</var> ≡ ±1 (mod <var>n</var>)}} so these trivial bases are often excluded.

[[Richard K. Guy|Guy]] mistakenly gives a definition with only the first condition, which is not satisfied by all primes.<ref>[[Richard K. Guy|Guy]], ''Pseudoprimes. Euler Pseudoprimes. Strong Pseudoprimes.'' §A12 in ''Unsolved Problems in Number Theory'', 2nd ed. New York: Springer-Verlag, pp. 27-30, 1994.</ref>