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Integers and Prime Relationship (Posted on 2015-09-27)

Find all integers k such that : gcd(4*M +1, k*M+1) = 1 for every integer value of M.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

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Proving the previous list of integers work

Comment 2 of 2 |

Perhaps I should prove that my previous answer, k = 4 +/- 2^n actually works

Well (4M + 1) is relatively prime to ((4 +/- 2^n)M + 1) if and only if it is also relatively prime to their difference, which is (+/- M*2^n)

And clearly it is. The only prime divisors of (+/- M*2^n) are 2 and prime factors of M. All of these leave a remainder of 1 when they divide (4M+1).

q.e,d.

Posted by Steve Herman on 2015-09-27 19:48:11

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