MAT 255 I. Let p and q be distinet prime mumbers and let a be an integer not divisible by p and not divisible by g. Show that the congruence *=a (mod py) has a unique solution modulo pq whenever the integer k is relatively prime to (p-1)(4-1).
Unitary Method
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Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
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i need the answer for each question separate please
![MAT 255
I. Let p and q be distinet prime mumbers and let a be an integer not divisible by p and tot divisible by
1. 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 congruence
a (umod n)
is solvable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b1412fc-5e24-47c1-805c-f79f0dfd1ed2%2F2ab3ebd7-e09f-4bd3-b70b-39b1dc04477c%2Ftx2oeyw_processed.jpeg&w=3840&q=75)
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