Prove that if gcd(m,n)=1 then m^phi(n)+n^phi(m)=congruent 1 (mod mn)

  1. 👍 0
  2. 👎 0
  3. 👁 213
  1. If GCD(a,r) = 1 then

    a^phi(r) = 1 mod r,


    m^phi(n)+n^phi(m) mod n = 1


    m^phi(n)+n^phi(m) mod m = 1

    So, mod(nm) it is 1.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. trigonometry

    if tan theta = 1/7 and tan phi= 1/3 then prove that cos 2 theta= sin 4 phi

    asked by ipshita on May 16, 2014
  2. geometry

    Supply the missing reasons to complete the proof Given: B congruent E and BC congruent to EC Prove: AC congruent to DC

    asked by Ryan on November 27, 2011
  3. trigonometry

    Rewrite 4sin(x)-5cos(x) as Asin(x+phi)

    asked by Anonymous on May 7, 2017
  4. math

    Please help me to find an equation for the tangent to the curve xsin2y=ycos2x at the point (phi/4, phi/2)

    asked by deel on August 13, 2012
  5. Maths: Partial Differentiation

    1) If x = rcos theta and y = r sin theta, show that partial r / partial x = cos theta and find partial theta / partial x. 2) If z = sin theta.sin phi.sin gamma, and z is calculated for the values theta = 30degrees, phi = 45

    asked by Claire on January 9, 2010
  1. confidentiality in allied health

    1. Which one of the following statements is an example of hearsay? "The report said the patient died on January 15." "I saw the doctor administer the injection." "I checked the patient's blood pressure three times." "The report

    asked by Anonymous on December 12, 2014
  2. Allied Health

    Under HIPAA, which one of the following statements is true regarding the release of PHI by covered entities to business associates? A. Covered entities are responsible for the use of PHI made by business associates. B. Covered

    asked by Andrew on April 20, 2009
  3. math

    RATES OF CHANGE QUESTION A spherical balloon is being blown up so that its volume is increasing by 0.6 m^3 s^-1. Find the rate at which the radius is increasing when the radius is 0.1 m. So what I did was that I determined dV/dt

    asked by tina on June 13, 2010
  4. Geometry

    Help! I'm so confused :( 1. Supply the missing reasons to complete the proof. Given: angle Q is congruent to angle T and line QR is congruent to line TR Prove: line PR is congruent to line SR Statement | Proof 1. angle Q is

    asked by Anonymous on December 17, 2017
  5. Discrete Math

    Let a, b, c, and d be integers, and let n be a positive integer. Prove that if a is congruent to c mod n and b is congruent to d mod n, then (a-b) is congruent to (c-d) mod n

    asked by Samantha on December 4, 2010
  6. precalculus PLEASE HELP!!

    Rewrite 4 sin(x) -1 cos(x) as A sin(x + phi) A= phi= -pi less than phi less than pi

    asked by anonymous on April 12, 2013

You can view more similar questions or ask a new question.