Please show your reasoning We now have our second attempt to develop a sound mat

Question

Please show your reasoning

We now have our second attempt to develop a sound mathematical proof. Prove that 3 is the only prime number which is one less than a perfect square. Note that you must both show that 3 is a prime number which is one less than a perfect square and show that there is no other prime number which is one less than a perfect square. A prime number is an integer n greater than 1 which is not a multiple of any positive number other than 1 or n. (Note that I is not a prime number A perfect squat is an integer m such that m = k2 for some integer k

Explanation / Answer

3 is a prime number since it is divisible by only itself

and 3 = 4 - 1

where 4 is a perfect square number since 2^2 = 4

now we need to prove that thre exist no other prime number which is 1 less than a perfect square number

let m = k^2 be a perfect square number

so we need to prove that m-1 is not a prime number

m - 1 = k^2 - 1 = (k +1)*(k -1)

so m-1 is divisible by atleast 2 more numbers apart from itself and 1 so m-1 is not a prime number

in case of 3 k-1 = (2 - 1) = 1

so 3 is only the prime number which is one less than a perfect square

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