▪ Ελληνική Μαθηματική Ολυμπιάδα "Αρχιμήδης" 1997

ΘΕΜΑΤΑ

1. Let be a point inside or on the boundary of a square . Find the minimum and maximum values of .

2.Let a function satisfy:

(i) is strictly increasing,
(ii) for all ,
(iii) for all .
Determine .

3. Find all integer solutions to
4. A polynomial with integer coefficients has at least distinct integer roots. Prove that if an integer is not a root of , then , and give an example for equality.

Πηγή: artofproblemsolving.com/