2007 iTest Problems/Problem 43: Difference between revisions
Created page with "== 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 spre..." |
Rockmanex3 (talk | contribs) m →Problem |
||
| Line 1: | Line 1: | ||
== 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 | 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 <math>9</math>-digit integers: | ||
<cmath>\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*} </cmath> | <cmath>\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*} </cmath> | ||
She notes that two of them have exactly <math>8</math> positive divisors each. Find the common prime divisor of those two integers. | She notes that two of them have exactly <math>8</math> positive divisors each. Find the common prime divisor of those two integers. | ||
== Solution == | == Solution == | ||
Revision as of 03:20, 16 June 2018
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 
-digit integers:
She notes that two of them have exactly 
positive divisors each. Find the common prime divisor of those two integers.
