PLEASE ONLY ANSWER PROBLEM 3. AND BEFORE ATTEMPTING TO ANSWER THEM, PLEASE READ THE INFORMATION BELOW, IT'S VERY IMPORTANT.

The following is my code for Part1, problem 2:

def isPrime(n): for i in range(2, n): if n % i == 0: return False return True def nPrimes(n): lst = [] i = 2 while i

print(nPrimes(200)) print(nPrimes(500)) The following is my code for part 3, problem 3:

def nPrimeLike(n): l = [] i = n m = 1 while i > 0: if (m**n)%n == m%n: l.append(m) i -= 1 m += 1 return l

print(nPrimeLike(200)) print(nPrimeLike(500))

FINALLY, PLEASE DO ALL THE CODES IN PYTHON AND USE LaTeX TYPESETTING FOR ANY MATH EQUATIONS USED IN THE CODES. AND REMEMBER, ONLY ANSWER QUESTION 3 FOR PART 3. CODING COULD BE DONE IN JUPYTER NOTEBOOK.

Part 3 Prime numbers satisfy another property. If one has three integers m, n and k we say m and n are congruent modulo k if the remainder from dividing m by A is the same as the remainder from dividing n by k. We can then write m n( mod k). For instance, the numbers 19 and 47 are congruent modulo 7 since 19-2 7+5 and 47-6 7 + 5. The remainder from division of both 19 and 47 by 7 is5 The congruence relation is preserved by arithmetic operations. If mn1( mod k) and m22 mod k), then mi +m2 nn2 mod k) and mm2 nin2 mod k) Prime numbers and congruences are related. There is a theorem that states: If p is a prime number, then ap a( mod p) for any integer p > a 0. For instance, for p 3, we observe 131 mod 3) 282 mod 3) 3273( mod 3) 4644 mod 3) Therefore, p 3 satisfies aamod p). Here, we have tried out a 1,2,3, 4 although 4 is not guaranteed to work. This relation does not in general hold true for composite numbers 1. Write a function listPrimeLike (n) which accepts n as an input and using the congruence returns the list of prime-like n relation check. umbers less than n 2. Write a function nPrimeLike (n) which accepts n as an input and re- turns the first n number of prime-like numbers using the congruence rela- tion Part 3 Prime numbers satisfy another property. If one has three integers m, n and k we say m and n are congruent modulo k if the remainder from dividing m by A is the same as the remainder from dividing n by k. We can then write m n( mod k). For instance, the numbers 19 and 47 are congruent modulo 7 since 19-2 7+5 and 47-6 7 + 5. The remainder from division of both 19 and 47 by 7 is5 The congruence relation is preserved by arithmetic operations. If mn1( mod k) and m22 mod k), then mi +m2 nn2 mod k) and mm2 nin2 mod k) Prime numbers and congruences are related. There is a theorem that states: If p is a prime number, then ap a( mod p) for any integer p > a 0. For instance, for p 3, we observe 131 mod 3) 282 mod 3) 3273( mod 3) 4644 mod 3) Therefore, p 3 satisfies aamod p). Here, we have tried out a 1,2,3, 4 although 4 is not guaranteed to work. This relation does not in general hold true for composite numbers 1. Write a function listPrimeLike (n) which accepts n as an input and using the congruence returns the list of prime-like n relation check. umbers less than n 2. Write a function nPrimeLike (n) which accepts n as an input and re- turns the first n number of prime-like numbers using the congruence rela- tion