If the remainder obtained by subtracting a number from its own square is 4 time the number, what is the number?

Translating the problem into an algebraic equation gives n squared minus n equals 4n. Factoring out n yields n squared minus 5n equals 0, so n multiplied by (n minus 5) equals 0. Since the number must be positive, we reject 0 and the number is 5. Verifying this, 5 squared is 25, and subtracting 5 gives 20, which is exactly 4 times 5.

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