What is the three-digit number which is 2 more than a perfect square and 2 less than a perfect cube?

1. Check 123: subtract 2 to get 121, and 121 = 11², a perfect square. 2. Add 2 to 123 to get 125, and 125 = 5³, a perfect cube. 3. Both conditions hold, so the number is 123. _Source: RRB Group D (RRC) PYQ, held 27-10-2013, Q.33._