MathDB

1

Part of 2008 Irish Math Olympiad

Problems(2)

Find All Primes Satisfying Given Equations

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

5/10/2008
Let p1,p2,p3 p_1, p_2, p_3 and p4 p_4 be four different prime numbers satisying the equations 2p_1 \plus{} 3p_2 \plus{} 5p_3 \plus{} 7p_4 \equal{} 162 11p_1 \plus{} 7p_2 \plus{} 5p_3 \plus{} 4p_4 \equal{} 162 Find all possible values of the product p1p2p3p4 p_1p_2p_3p_4
number theoryprime numbersnumber theory proposed
Find All Triples (a,b,c) of Integers

Source: Irish Mathematical Olympiad - Paper 2 - 2008 -Question 1

5/11/2008
Find, with proof, all triples of integers (a,b,c) (a,b,c) such that a,b a, b and c c are the lengths of the sides of a right angled triangle whose area is a \plus{} b \plus{} c
geometrynumber theory proposednumber theory