Question

Let a and b be the leg lengths of a right triangle, and let c be the length of the hypotenuse. If all three are natural numbers, and a is an odd prime number, prove that the number 2(a+b+1) is a square of some natural number.

Answer 1

this has been proven to be true

Explanation:

from pythagoras theorem, we know that for any right angkd triangle

a²+b² = c²

if a is an odd number as well as a prime number,

a= 3

b = 4

such that

2(a+b+1) = 2(3+4+1) = 2 * 8 = 16

16 is a square of 4.

also if a = 5 and b = 2

2(5+2+1) = 2*8 = 16

16 is a square of 4

so this has been proven to be true for the odd and prime numbers of a.