MathDB

1

Part of 2009 Junior Balkan Team Selection Test

Problems(2)

Expressing number as a sum of 2 squares

Source: Serbian JBTST 1, Day 1

5/30/2009
Given are natural numbers a,b a,b and n n such that a^2\plus{}2nb^2 is a complete square. Prove that the number a^2\plus{}nb^2 can be written as a sum of squares of 2 2 natural numbers.
algebrasystem of equationsalgebra proposed
Easy divisibility

Source: Serbian JBTST 1, Day 2

5/31/2009
Find all two digit numbers AB‾ \overline{AB} such that AB‾ \overline{AB} divides A0B‾ \overline{A0B}.
number theory proposednumber theory