Prime = Square?

Number Theory Level 1

How many prime numbers are also perfect squares ?

0 1 Infinitely many 4

Chung Kevin by Chung Kevin , 46, Australia

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3 solutions

Mohammad Khaza
Aug 4, 2017

prime numbers can not be square of other numbers.as it is only divided by 1 and itself.

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Prince Loomba
Sep 4, 2016

Being a prime number implies only 2 factors. Thus 1 is ruled out. If the number is square of a number, the square root will also be a factor, making it the 3rd factor and a contradiction. So no prime number is a square

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But that isn't true for the case of 1.

Chung Kevin - 4 years, 9 months ago

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We already assume 2 factors. 1 gets ruled out at first statement. Contradicition is for remaining numbers!

Prince Loomba - 4 years, 8 months ago

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Yes, but that isn't written down in your solution. You have to explain why "1, the square root, the number itself" are distinct, in order to conclude that we have (at least) 3 factors.

Chung Kevin - 4 years, 8 months ago

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@Chung Kevin – Added 1 line.

Prince Loomba - 4 years, 8 months ago

Trivial fact: a perfect square is a number that is expressed as the product of two equal numbers, thus never making it a prime number. Period.

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