Question

suppose p is a prime number and p2 divides ab and gcd(a,b)=1. Show p2 divides a...

suppose p is a prime number and p2 divides ab and gcd(a,b)=1. Show p2 divides a or p2 divides b.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show if p >1 and p divides (p -1)! + 1, then p is prime.    I...
Show if p >1 and p divides (p -1)! + 1, then p is prime.    I need a direct proof.  
prove that if gcd(a,b)=1 then gcd (a-b,a+b,ab)=1
prove that if gcd(a,b)=1 then gcd (a-b,a+b,ab)=1
A natural number p is a prime number provided that the only integers dividing p are...
A natural number p is a prime number provided that the only integers dividing p are 1 and p itself. In fact, for p to be a prime number, it is the same as requiring that “For all integers x and y, if p divides xy, then p divides x or p divides y.” Use this property to show that “If p is a prime number, then √p is an irrational number.” Please write down a formal proof.
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a,...
4. Let a, b, c be integers. (a) Prove if gcd(ab, c) = 1, then gcd(a, c) = 1 and gcd(b, c) = 1. (Hint: use the GCD characterization theorem.) (b) Prove if gcd(a, c) = 1 and gcd(b, c) = 1, then gcd(ab, c) = 1. (Hint: you can use the GCD characterization theorem again but you may need to multiply equations.) (c) You have now proved that “gcd(a, c) = 1 and gcd(b, c) = 1 if and...
Given that the gcd(a, m) =1 and gcd(b, m) = 1. Prove that gcd(ab, m) =1
Given that the gcd(a, m) =1 and gcd(b, m) = 1. Prove that gcd(ab, m) =1
41. Suppose a is a number >1 with the following property: for all b, c, if...
41. Suppose a is a number >1 with the following property: for all b, c, if a divides bc and a does not divide b, then a divides c. Show that a must be prime. 44. Prove that for all numbers a, b, m, if (a, m) = 1 and (b, m) = 1, then (ab, m) = 1. 46. Prove that for all numbers a, b, if d = (a, b) and ra + sb = d, then (r,...
Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that...
Prove that for positive integers a and b, gcd(a,b)lcm(a,b) = ab. There are nice proofs that do not use the prime factorizations of a and b.
Let m be a natural number larger than 1, and suppose that m satisfies the following...
Let m be a natural number larger than 1, and suppose that m satisfies the following property: For any integers a and b, if m divides ab, then m divides either a or b (or both). Show that m must be prime.
use the fundamental theorem of arithmetic to prove: if a divides bc and gcd(a,b)=1 then a...
use the fundamental theorem of arithmetic to prove: if a divides bc and gcd(a,b)=1 then a divides c.
1. Let p be any prime number. Let r be any integer such that 0 <...
1. Let p be any prime number. Let r be any integer such that 0 < r < p−1. Show that there exists a number q such that rq = 1(mod p) 2. Let p1 and p2 be two distinct prime numbers. Let r1 and r2 be such that 0 < r1 < p1 and 0 < r2 < p2. Show that there exists a number x such that x = r1(mod p1)andx = r2(mod p2). 8. Suppose we roll...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT