# coprime

1. ### coprime numbers

2m-3 and 10m-15 are coprime integers.Which of the choices from below is coprime with each one of the numbers? a)3m-1 b)m+4 c)2m+6 d)m+3 e)5m Answer is b. I couldn't find the answer. First of all both numbers are not coprime. When we divide them with each other we get 5 or 1/5.
2. ### X, Y, Z are coprime integers. 1/x + 1/y = 1/z. Prove that (X+Y) is a square number.

Okay, so I'm stuck on this for an hour now, so I'd really appreciate some help, please: X, Y, Z are coprime integers. We also know that 1/x + 1/y = 1/z. Prove that (X+Y) is a square number. ----- This should be entry level university math, but I'm stuck with it. I hope I posted to the right...
3. ### pairwise coprime and fundamental theorem of arithmetic

I have added a attachment of my question that I am stuck on. How would you solve it? Thank you
4. ### proof of coprime numbers

i have the question 'prove that if a and b are coprime, then ab and a+b are also coprime.' i have no idea where to start.. ?
5. ### coprime problem

pls solve this problem for me as m not also to solve it... question: suppose a and b are relatively prime. prove that ab and a+b are relatively prime...
6. ### prove v and u ortogonal using coprime polynomials

Hi Can't figure out the direction to solve the following question: Given: 1. T normal transformation in finitly created vector space F with inner dot product defined on it. 2. M1(t) and M2(t) two coprime polynomials. 3. let u,v be two vectors in F such that M1(T)u=0 and M2(T)v=0 (T is...
7. ### coprime

how do you show that 2 consecutive integers are coprime? i know we need to show that gcd is 1 where they have opp parity
8. ### Show co-prime...

Suppose that a,b\in\mathbb{N}^+,\ \gcd(a,b) = 1 and p is an odd prime. Show that \gcd\left(a+b,\frac{a^p+b^p}{a+b}\right) \in\{1,p\}
9. ### Coprime Question

On page 67 here -> http://www1.spms.ntu.edu.sg/~frederique/AA10.pdf I understand why InJ is a subset of IJ right up to ax + ay is an element of IJ. I figured that ax + ay = yx + xy (since a is in I and a is in J) so we have xy and yx are in IJ... but how do we know that when you add two...
10. ### Coprime elements

Let \mathbb{Z}_{p^r} = \{ 0,1, \ldots, p^r -1\} be the ring of integers modulo p^r, a power of a prime. I was wondering if someone could help explain why there are p^{r-1} elements that are coprime to p^r in this ring? I am getting tangled up in knots and would appreciate any help with this...
11. ### coprime question!

some how using the fact that integers a and b are coprime if, and only if, there exist integers m and n such that am + bn = 1 i am trying to find: m and n to show that (i) 41 and 68 are coprime, (ii) 71 and 118 are coprime. i also have to prove: 3k + 2 and 5k + 3 are coprime for all k\in...
12. ### Coprime numbers

Prove, that if (m,n) = 1 // m and n are two different primes then (2^m -1, 2^mn -1/2^m -1) = 1
13. ### If r is a rational solution r = p/q and p and q are coprime, show that q|an and p|a0.

Suppose that r is a solution of the equation: anxn + a(n−1)x(n−1) + . . . + a1x + a0 = 0 where the coefficients ak belongs to Z for k = 0, 1, . . . n, and n is greater or equal to 1. If r is a rational solution r = p/q, where p, q belong to Z and p and q are coprime, show that q|an and p|a0...
14. ### Coprime Test

I read two numbers a and b are coprime if b^{a - 1} = 1 (mod a). Is it me or does this test not hold when a = 6 and b = 5, which are coprime? 5^{6 - 1} = 1 (mod 6) 5^5 = 1 (mod 6) 3125 = 1 (mod 6) 3125 mod 6 is 5, which does not equal 1, so the test fails. Is it me or the test?
15. ### Numbers in array and its exponents ( congruence operation )

Introduction: ============= Another way to see congruences is to put the numbers in an array of width n. In the following example n is 5: col 1 2 3 4 5 -------------------------- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19...
16. ### Another coprime proof

Hi all, Prove that if gcd(a,m) = gcd(b,m) = 1 then gcd(ab,m) = 1.
17. ### Coprime Proof

Hi all, a, b are coprime integers such that a|m and b|m, for some integer m. Prove, using Euclid’s lemma, that ab|m.
18. ### Proof with coprimes

Hi, I have this question and I have no idea where to start. Can anyone please just give me a nudge in the right direction? Let a, b and c be integers. Suppose (a,b) = 1 and c divides a+ b. Show that (a,c) = 1 and (b, c) = 1. I've made a couple of notes like: sa + tb = 1 and a+b=cd for some...
19. ### coprime

Let n \in \mathbb{N}. Are n and n+1 relatively prime? How about n and n^2+1? My answer is yes, both (n,n+1)=1 and (n, n^2+1)=1. But is there a way to show these are true?
20. ### Coprime Theorem II

Let a<b<c be positive, pairwise relatively prime integers, i.e. (a,b)=(b,c)=(a,c)=1 Without loss of generality, show that (a^2bc , ax+1)=1, where x=(-a-b-c)(ab+bc+ac)^{-1} (\bmod abc) . Note: I have already shown that gcd(ab+bc+ac , abc)=1, so x is well-defined. See...