MathDB

4

Part of 2009 JBMO Shortlist

Problems(2)

tiling a table mxn with corner figures

Source: JBMO 2009 Shortlist C4

10/14/2017
Determine all pairs of (m,n)(m, n) such that is possible to tile the table m×n m \times n with figure ”corner” as in figure with condition that in that tilling does not exist rectangle (except m×nm \times n) regularly covered with figures.
JBMOcombinatorics
p_1^2+ p_2^2+ ... + p_{12}^2 = p_{13}^2

Source: JBMO 2009 Shortlist N4

10/14/2017
Determine all prime numbers p1,p2,...,p12,p13,p1≤p2≤...≤p12≤p13p_1, p_2,..., p_{12}, p_{13}, p_1 \le p_2 \le ... \le p_{12} \le p_{13}, such that p12+p22+...+p122=p132p_1^2+ p_2^2+ ... + p_{12}^2 = p_{13}^2 and one of them is equal to 2p1+p92p_1 + p_9.
JBMOnumber theorySum of powers