IMO 1979 LL FIN18

Show that for no integers a \geq1, n \geq1 is the sum

IMO 1979 LL FIN18

Origin: FIN

Problem

Show that for no integers a \geq1, n \geq1 is the sum 1 + 1 + a + 1 + 2a + \cdot \cdot \cdot + 1 + na an integer.