IMO Shortlist 1969 problem 17
Dodao/la:
arhiva2. travnja 2012. ![(CZS 6)](/media/m/8/0/2/80279aa92fc8addbbcea89436dedce61.png)
Let
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
and
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
be two real numbers. Find the first term of an arithmetic progression
![a_1, a_2, a_3, \cdots](/media/m/e/f/7/ef7e4771a56d61634b464caabb138f2d.png)
with difference
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
such that
![a_1a_2a_3a_4 = p.](/media/m/7/6/f/76fb27a5dde3405a6e8d57ad31a07c16.png)
Find the number of solutions in terms of
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
and
%V0
$(CZS 6)$ Let $d$ and $p$ be two real numbers. Find the first term of an arithmetic progression $a_1, a_2, a_3, \cdots$ with difference $d$ such that $a_1a_2a_3a_4 = p.$ Find the number of solutions in terms of $d$ and $p.$
Izvor: Međunarodna matematička olimpijada, shortlist 1969