MAT 255I. Let p and q be distinet prime mumbers and let a be an integer not divisible by p and tot divisible by1. Show that the congruence=a (mod py)has a unique solution modulo pg whenever the integer k is relatively prime to (p-1)(4- 1).2. Give an example illustrating the result above.3. Generalize the result in Problem I to the case of the congruence(mod pipaPs-p)where p.Pa, Pi are distinet primes. Prove your generalized result.4. Use the result in Problem 3 and state conditions on n, a, and k under which the congruencea (umod n)is solvable.

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MAT 255 Let p and q be distinet prime mumbers and let a be an integer not divisible by p and not divisible by q. Show that the congruence =a (mod p) has a unique solution modulo pg whenever the integer k is relatively prime to (p-1)(q-1).

MAT 255 Let p and q be distinet prime mumbers and let a be an integer not divisible by p and not divisible by q. Show that the congruence =a (mod p) has a unique solution modulo pg whenever the integer k is relatively prime to (p-1)(q-1).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 39E

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