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can a number 100 zeros 100 ones 100 twos is a perfect square? Prove it.

Note by Royston Dsouza 2 years, 2 months ago

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No. Hint:- Look at divisibility by 3 and 9.

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Digit sum of the number is \( 300 \). Therefore, it is divisible by 3, since 3 divides 300. But it is not divisible by 9, since 9 does not divide 300. Since the number is divisible by 3 but not 9, it can't be a perfect square/

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TopNewestNo. Hint:- Look at divisibility by 3 and 9.

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How does it help?

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Digit sum of the number is \( 300 \). Therefore, it is divisible by 3, since 3 divides 300. But it is not divisible by 9, since 9 does not divide 300. Since the number is divisible by 3 but not 9, it can't be a perfect square/

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