MathDB

4

Part of 2008 Canada National Olympiad

Problems(1)

Function on the natural numbers

Source: 40th Canadian Mathematical Olympiad

4/21/2008
Determine all functions f f defined on the natural numbers that take values among the natural numbers for which (f(n))^p \equiv n  {\rm mod}\; f(p) for all nāˆˆN n \in {\bf N} and all prime numbers p p.
functionmodular arithmeticnumber theoryprime numbersnumber theory unsolved