MathDB

1

Part of 2013 European Mathematical Cup

Problems(2)

Product of first m primes

Source: European Mathematical Cup 2013, Junior Division, P1

7/3/2014
For m∈Nm\in \mathbb{N} define m?m? be the product of first mm primes. Determine if there exists positive integers m,nm,n with the following property : m?=n(n+1)(n+2)(n+3) m?=n(n+1)(n+2)(n+3)
Proposed by Matko Ljulj
number theory proposednumber theory
Tables in which each entry is the product of its neighbors

Source: 2nd European Mathematical Cup, Problem 1

12/16/2013
In each field of a table there is a real number. We call such n×nn \times n table silly if each entry equals the product of all the numbers in the neighbouring fields.
a) Find all 2×22 \times 2 silly tables. b) Find all 3×33 \times 3 silly tables.
linear algebramatrixalgebra proposedalgebra