Prove that for every natural number n, fraction 21 n + 4 14 n + 3 is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I cannot get it from thereon.

Question

Prove that for every natural number n, fraction             21      n      +      4              14      n      +      3       is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I cannot get it from thereon.

Mollie Roberts · Accepted Answer

Going by Euclidean algorithm:  G  C  D  (  21  n  +  4  ,  14  n  +  3  )  =  G  C  D  (  7  n  +  1  ,  14  n  +  3  )  =  G  C  D  (  7  n  +  1  ,  1  )  =  1

Azzalictpdv · Accepted Answer

21  n  +  4  =  (  14  n  +  3  )  +  7  n  +  1  14  n  +  3  =  2  (  7  n  +  1  )  +  1

Prove that for every natural number n, fraction 21 n + 4

Answered question

Answer & Explanation

New Questions in Pre-Algebra