MathDB

A natural number

n

is called "

k

-squared" if it can be written as a sum of

k

perfect squares not equal to 0.
a) Prove that 2020 is "

2

-squared" , "

3

-squared" and "

4

-squared".
b) Determine all natural numbers not equal to 0 (

a, b, c, d ,e

)

a<b<c<d<e

that verify the following conditions simultaneously :
1)

e-2

e

e+4

are all prime numbers. 2)

a^2+ b^2 + c^2 + d^2 + e^2

= 2020.

Problem Statement