Math 312 Solutions To Practice Problems Worksheet With Answers Page 3
ADVERTISEMENT
1
2
33
there were only finitely many primes of the form 6k + 5, say
p
= 5 < p
< p
<
< p .
0
1
2
Consider the integer
N = 6p
p
p + 5.
1
2
Clearly N > 1 is not divisible by 2 and the note with which we began
this solution implies that N has at least one prime divisor p of the form
6k + 5. If p = 5, we get that
5 N
5 = 6p
p
p ,
1
2
while, if p > 5, we have that
5 N
6p
p
p = 5.
1
2
In either case, we have a contradiction.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education