Chapter 12 - Further Topics in Diophantine Equations.sagews

Chapter 12 - Further Topics in Diophantine Equations

The abc Conjecture ####

We make use of the radical_value command to compute the product of the prime divisors of a number:

factor(40).radical_value()

10

We now use this command to search for counterexamples to (12.37)

for a in range(1,51):
    for b in range(a,51):
        if gcd(a,b)==1:
            rad=factor(a*b*(a+b)).radical_value()
            if rad < a+b:
                print(a,b,a+b,rad)

(1, 8, 9, 6) (1, 48, 49, 42) (5, 27, 32, 30) (32, 49, 81, 42)

︠86cdaf8e-4643-41b8-be83-e0b72262b3ed︠