MathDB

1

Part of 2007 Pan African

Problems(2)

Sum of digits of N and N+1

Source: PAMO 2007 Q1

12/10/2013
Find all natural numbers NN consisting of exactly 11121112 digits (in decimal notation) such that: (a) The sum of the digits of NN is divisible by 20002000; (b) The sum of the digits of N+1N+1 is divisible by 20002000; (c) 11 is a digit of NN.
modular arithmeticnumber theory unsolvednumber theory
System of equations involving square roots

Source: PAMO 2007 Q4

12/10/2013
Solve the following system of equations for real x,yx,y and zz: \begin{eqnarray*} x &=& \sqrt{2y+3}\\ y &=& \sqrt{2z+3}\\ z &=& \sqrt{2x+3}. \end{eqnarray*}
algebrasystem of equationsalgebra unsolved