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1

Part of 2013 Greece Team Selection Test

Problems(2)

Equation in natural numbers.

Source: Greek IMO TST 2013,Pr.1

8/16/2014
Find all pairs of non-negative integers (m,n)(m,n) satisfying n(n+2)4=m4+m2−m+1\frac{n(n+2)}{4}=m^4+m^2-m+1
number theory proposednumber theory
Determine whether it is irreducible

Source: 2013 Greek 2nd TST,Pr.1

5/24/2016
Determine whether the polynomial P(x)=(x2−2x+5)(x2−4x+20)+1P(x)=(x^2-2x+5)(x^2-4x+20)+1 is irreducible over Z[X]\mathbb{Z}[X].
algebrapolynomial