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2013 and Perfect Square Settlement (Posted on 2023-06-25) Difficulty: 3 of 5
We know that 2025 = 452. Therefore, 2025 is a perfect square in base ten.

Determine all positive integer value of N greater than 3, for which 2013 base N is a perfect square.

Provide valid reasoning for your answer.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution solution Comment 3 of 3 |
2013 in base 6 is 441 which is 21^2

----------
big = 1000
sqroot = int((2*big**3 + big + 3)**.5)
squares = [i*i for i in range(sqroot + 1)]
for x in range(big):
    if 2*x**3 + x + 3 in squares:
        print(x, 2*x**3 + x + 3, int((2*x**3 + x + 3)**.5))

OUTPUT:   6 441 21

  Posted by Larry on 2023-06-26 11:49:15
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