[Hints] 2014 Singapore MO (Junior Rd 1) Problem 29

2014 SMO (Junior-Rd1) 29. Let N = \overline{abcd} be a 4-digit perfect square that satisfies \overline{ab} = 3 \cdot \overline{cd} + 1. Find the sum of all possible values of N.

(The notation n = \overline{ab} means that n is a 2-digit number and its value is given by n = 10a + b.)

Perfect squares can only end with certain digits, and can only have certain remainders in certain modulo bases. Use that to narrow the number of cases that you have to check.

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