91Ó°ÊÓ

Use Fermat's method to factor each of the following numbers: (a) \(2279 .\) (b) 10541 . (c) 340663 [Hint: The smallest square just exceeding 340663 is \(584^{2}\).]

From Fermat's theorem deduce that, for any integer \(n \geq 0,13 \mid 11^{12 n+6}+1\).

Show that \(18 !=-1(\bmod 437)\).