Question

The sum of squares of first 7 prime number also satisfy the Lagrange’s Four Square theorem which states that “Every positive integer can be expressed as the sum of four squares”. What is the number I am talking about?
(a) 666
(b) 484
(c) 1089
(d) 6178

Answer 1

The sum of squares of 7 prime number is 484

Answer 2

Concept:

Lagrange’s Four Square theorem states that “Every positive integer can be expressed as the sum of four squares”.

Given:

We have,

To use the first 7 prime numbers.

Find:

We are asked to find the number.

Solution:

So,

We have,

According to the question,

The First 7 prime numbers are,

2, 3, 5, 7, 11, 13, 17

So,

Now,

The Sum of squares of these First 7 prime numbers are,

i.e.

2² + 3² + 5² + 7² + 11² + 13² + 17²

= 4 + 9 + 25 + 49 + 121 + 169 + 289

We get,

666

Also, it satisfies the Lagrange’s Four Square theorem.

As the sum of squares is expressed as a positive number or vice versa.

Hence, the number is 666.

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