My Three Digits

Pro Problems > Math > Number and Quantity > Number Theory > Digits

My Three Digits

I'm thinking of a three-digit number. The sum of my number's first and last digits is a perfect square. The sum of my number's first and second digits is also a perfect square. If my third digit is subtracted from my second digit, the result is 5. If my number is not a multiple of three, and it has no repeated digits, what is my number?

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Problem by Mr. Twitchell

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If you subtract my third digit from my first digit, you get a perfect square.

Oh, by the way, I'm a perfect square.

What year am I?