Prove that the square root of a Mersenne number (

Jaqueline Kirby 2022-06-06 Answered
Prove that the square root of a Mersenne number ( k = 2 n 1) is irrational.
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Answers (1)

iceniessyoy
Answered 2022-06-07 Author has 27 answers
All perfect squares are either 1 or 0 mod 4. Writing 2 n 1 in binary, we get 1111...11, and when you divide that by 4, which is using only the two right most digits (the rest of the digits are a multiple of 100), it's clear that all Mersenne numbers are 3 mod 4, except when n = 0 , 1.
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