Prove it if it is true or give counterexample if it is false:let a , b , k ∈ Z and n is positive integer, if a ≡ b ( mod n ) then k a ≡ k b ( mod n )My try: it is false statement like if − 3 ≡ 2 ( mod 5 ) then 3 − 3 ≢ 3 2 ( mod 5 )

Question

Prove it if it is true or give counterexample if it is false:let   a  ,  b  ,  k  ∈  Z and   n is positive integer, if   a  ≡  b  (    mod      n  ) then       k    a    ≡      k    b    (    mod      n  )My try: it is false statement like if   −  3  ≡  2  (    mod      5  ) then       3          −      3        ≢      3    2    (    mod      5  )

Tania Alvarado · Accepted Answer

You should work out the calculation       3    2    ≡  4    (  mod    5  )      3          −      3        =  (      3    3        )          −      1        ≡      2          −      1        ≡  3    (  mod    5  ) to show they disagree. The correct statement is Euler&#039;s theorem if   a  ≡  b    (  mod    ϕ  (  n  )  ) then       k    a    ≡      k    b      (  mod    n  ) where   ϕ  (  n  ) is Euler&#039;s totient function.

Prove it if it is true or give counterexample if it is false: let a,b,k∈Z and n is positive integer, if a≡b(modn) then k^a≡k^b(mod n)

Answered question

Answer & Explanation

New Questions in College Statistics