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Number Theory Level 1

$\large \color{#20A900} {\text{True}}$ $\large or$ $\large \color{#D61F06}{False}$ $\large ?$

All positive prime numbers can be written as the sum of two or more perfect square numbers.

This is a Number is all around series problem.

Try out all of my problem.

True False

3 solutions

Md Mehedi Hasan
Nov 9, 2017

Relevant wiki: Perfect square

I use addition of two or more perfect square number to describe a prime number.

All prime number can be expressed thus.

$1$ is a perfect square.

With this help, some example is: $2=1^2+1^2\\3=1^2+1^2+1^2\\5=2^2+1^2\\7=2^2+1^2+1^2+1^2\\11=3^2+1^2+1^2\\\vdots\quad\vdots\quad\vdots$

Saksham Jain
Nov 10, 2017

Because we can use 1 therefore answer is true

Xin Ze Cai
Sep 15, 2019

Let the prime number be represented as p .

$\frac{p}{1}$ = p.

1 squared = 1.

Therefore, we can use the square of 1, p times until we reach the prime number.

E.g., 2017 = 1+1+1+1+1...+1+1+1 (2017 times).