MathDB

2

Part of 2011 India IMO Training Camp

Problems(2)

Indian TST Algebra

Source: Selection Test 2

6/20/2011
Suppose a1,…,ana_1,\ldots,a_n are non-integral real numbers for n≥2n\geq 2 such that a1k+…+ank{a_1}^k+\ldots+{a_n}^k is an integer for all integers 1≤k≤n1\leq k\leq n. Prove that none of a1,…,ana_1,\ldots,a_n is rational.
calculusintegrationalgebra unsolvedalgebra
No integer of form n^7 + 7 is a perfect square

Source: USA TST 2008, Day 2, Problem 4

12/25/2005
Prove that for no integer n n is n^7 \plus{} 7 a perfect square.
algebraPerfect Squarenumber theoryTSTUSAHi