1

Part of 1998 Polish MO Finals

Problems(2)

equations in a,b,c,x,y,z

Source:

Find all solutions in positive integers to: \begin{eqnarray*} a + b + c = xyz \\ x + y + z = abc \end{eqnarray*}

algebra unsolvedalgebra

infinitely many muplitples of 7 in a sequence

Source:

Define the sequence

a_1, a_2, a_3, ...

a_1 = 1

a_n = a_{n-1} + a_{[n/2]}

. Does the sequence contain infinitely many multiples of

7

number theory unsolvednumber theory