MathLabs

Problem 1

Prove that the fraction 21n+414n+3\frac{21n+4}{14n+3} is irreducible for every natural number nn.
Step 1 of 4: Define the common divisor
d=gcd⁡(21n+4,14n+3)d=\gcd(21n+4,14n+3)
Detailed analysis

Let d=gcd⁡(21n+4,14n+3)d=\gcd(21n+4,14n+3). To prove the fraction is irreducible, it is enough to show that this positive common divisor must equal 11.