## Problem of the Day #133: The Three SophomoresJuly 30, 2011

Posted by Seungln in : potd , trackback

Victoria, Veronica and Ivy are playing a number game.

Victoria is thinking of a number that is congruent to $307 \pmod{821}$. Veronica is thinking of a number that is congruent to $283 \pmod{797}$. Ivy is thinking of a number that is congruent to $383 \pmod{877}$. They tell each other what their number is, and, to their surprise, they find out that they all thought of the same number.

If the number they thought of is a positive integer less than $100000000000$, what is the greatest number for which this could happen?