Proving that for each prime number p , the

Makayla Boyd

Makayla Boyd

Answered question

2022-06-13

Proving that for each prime number p, the number p is irrational.

Answer & Explanation

Korotnokby

Korotnokby

Beginner2022-06-14Added 19 answers

If p = a b where ( a , b ) = 1 and a > 1 as p > 1,
then p = a 2 b 2 .
Now as p is integer, b 2 must divide a 2 , which is impossible unless b = 1 as ( a , b ) = 1.
If b = 1, p = a 2 which can not be prime as a > 1.

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