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Number Theory Level 2

How many statements are true about the number 2017?

  • It is a prime number.

  • It can be written as a sum of two perfect squares.

  • It is a Fibonacci number.

  • It has only 3 divisors.

4 0 2 1 3

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Tommy Li
Sep 30, 2017

1 s t 1^{st} statement is correct .

2 n d 2^{nd} statement is correct . ( 4 4 2 + 9 2 = 2017 ) (44^2+9^2 =2017)

3 r d 3^{rd} statement is incorrect .

4 t h 4^{th} statement is incorrect . ( 2017 2017 is a prime )

⇒ \Rightarrow 2 statements are correct

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Is there a more efficient for finding the solution to statement 2 than just experimenting?

Ron Lauterbach - 3 years, 8 months ago

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It is proven that a prime p p is expressible as the sum of two squares if and only if p ≡ 1 m o d 4 p\equiv 1\mod 4 ( Fermat's theorem )

Marco Brezzi - 3 years, 8 months ago

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