2007 iTest Problems/Problem 43

Revision as of 04:20, 16 June 2018 by Rockmanex3 (talk | contribs) (Problem)

Problem

Bored of working on her computational linguistics thesis, Erin enters some three-digit integers into a spreadsheet, then manipulates the cells a bit until her spreadsheet calculates each of the following one hundred $9$-digit integers:

\begin{align*}700\cdot 712\,\cdot\, &718+320,\\701\cdot 713\,\cdot\, &719+320,\\ 702\cdot 714\,\cdot\, &720+320,\\&\vdots\\798\cdot 810\,\cdot\, &816+320,\\799\cdot 811\,\cdot\, &817+320.\end{align*}

She notes that two of them have exactly $8$ positive divisors each. Find the common prime divisor of those two integers.

Solution