MathDB

3

Part of 2008 Irish Math Olympiad

Problems(2)

When Is Given Product A Square?

Source: Irish Mathematical Olympiad - Paper 1 - 2008 -Question 3

5/10/2008
Determine, with proof, all integers x x for which x(x\plus{}1)(x\plus{}7)(x\plus{}8) is a perfect square.
number theory proposednumber theory
Show the Given Sequence is Unique

Source: Irish Mathematical Olympiad - Paper 2 - 2008 -Question 3

5/11/2008
Find a3,a4,...,a2008 a_3,a_4,...,a{}_2{}_0{}_0{}_8, such that ai=±1 a_i =\pm1 for i=3,...,2008 i=3,...,2008 and ∑i=32008ai2i=2008 \sum\limits_{i=3}^{2008} a_i2^i = 2008 and show that the numbers a3,a4,...,a2008 a_3,a_4,...,a_{2008} are uniquely determined by these conditions.
number theory proposednumber theory