Math, asked by jddjdiodeo, 1 year ago

Prove that a positive integer n is prime number,if no prime p less than or equal to √n divides n

Answers

Answered by sushilkumaragr468
1

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Let any integer n ≥ 0 is a composite number.

so, n has a factor between 1 to n.


Let r is the factor of n, such that, 1 < r < n


so, we can write n = rs , where r and s are positive integers such that, 1 < r, s < n


assume , integer r is greater than equal to s.

e.g., r ≤ s


And also consider s > √n


so, √n < s ≤ r


it means, r > √n


but n = rs > √n. √n


so, n > n which is a contradiction.

hence, our assumption was wrong.

therefore, a positive integer n is prime number,if no prime p less than or equal to √n divides n

Answered by ravi34287
5
thank

hope it helps..........
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