Question

How many primes cannot be expressed as a difference of squares of two natural numbers?
1.0
2.1
3. 2
4.3
5. More than 3​

Answer 1

Step-by-step explanation:

only the prime no. 2 can't be expressed as difference of two natural numbers.

let us assume,

p=a^2-b^2, where p is a prime number

p=(a+b)(a-b)

p=p*1

and no other factors of p can be made (in terms of natural numbers)

since, a,b are distinct natural numbers,

therefore, a+b and a-b is also natural number

p*1=(a+b)(a-b)

a+b>a-b(a>0)

therefore, a-b=1,a+b=p

a=b+1

b+b+1=p

2b+1=p

p=odd

no even p can be expressed as this

only 2 is even prime

therefore,only 1 prime number can't be expressed as difference of two natural numbers.