Exercise
Which of the following statements is true?
If a divides bcd and
a and b are relatively prime, then a divides c
or d
If a divides bcd, and
if a and b as well as a and c are relatively prime,
then a divides d
If a does not divide bc, then a is relatively prime with b or c
No, a = 4, b = 3, c = 2 and d = 2 is a counterexample
Yes, this is true since also a and bc are relatively prime.
For, if xa + yb = 1 and ua + vc = 1,
then 1 = (xa + yb) · (ua + vc)
= (xua + xvc + uyb) a + yv bc
What about a = 8 and b = c = 2