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2013 and Perfect Square Settlement (Posted on 2023-06-25)

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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computer solution

| Comment 1 of 3

for b=4:10000

r=2*b^3+b+3;

sr=round(sqrt(r));

if sr^2==r

disp([b r sr])

end

finds

6 441 21

i.e., in base 6, 2013 represents 441 (base 10), whose square root is 21.

Posted by Charlie on 2023-06-25 16:42:37

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