Using the link below, you can download the latest version of Magento 1.9.x
https://magento.com/tech-resources/download
On this page, you can find both the latest version of 1.9.x and Magento 2.x.x
Magento 1.9.x on Github.com, OpenMage :
https://github.com/OpenMage/magento-mirror
Update to Magento 1.9.3.1 no results on search