Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# Problem K. 442. (December 2014)

K. 442. Consider the set of the numbers 1, 3, 120. The product of any two of them is one smaller than a perfect square. Which positive integer less than 120 may be added to the set so that the four numbers should still have this property?

(6 pont)

Deadline expired on January 12, 2015.

### Statistics:

 89 students sent a solution. 6 points: Benda Orsolya, Csizmadia Róbert, Csuha Boglárka, Dalnoki Laura, Dévény Csaba, Dömötör Emőke, Encz Koppány, Farkas Ádám, Farkas Lilla, Farkas Panka, Fekete Balázs Attila, Hegedűs 330 Marcell, János Zsuzsa Anna, Kaló Eszter, Kollár Johanna, Koronczi Fanni, Korpás Isabel, Kovács 124 Marcell, Kubovics Márton, Lakatos Ágnes, Maksa Gergő, Márton Anna, Mészáros Melinda, Németh 962 Ambrus, Németh Csilla Márta, Németh Gergő, Orbán Sára, Öcsi Rebeka, Páhoki Tamás, Pécsi 117 Ildikó, Rimai 217 Dániel, Sepp Márton, Slenker Balázs, Szabadkai Beatrix, Szabó022 Eszter, Szarka Álmos, Tamási Kristóf Áron, Thuróczy Mylan, Tószegi Fanni, Valkó Bence, Varga 274 Tamás. 5 points: Agócs Katinka, Fekete Zsófia, Valentiny Anett, Wenhardt Kata. 4 points: 9 students. 3 points: 12 students. 2 points: 13 students. 1 point: 6 students. 0 point: 2 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, December 2014