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Elementary Number Theory | Congruence

If a ≡ b mod(n) and b ≡ c mod(n) , then
Necessary condition to apply the Chinese remainder theorem is modulo of congruence should be:
For any integers a and b, and positive integer n, choose the incorrect statement:
If p is a prime then for any integer a 
If a and b are any positive integers and a ≡ b(mod n) then 
If m and n are positive integers with m and n are relatively prime then, mϕ (n) + nϕ (m) is congruent to
The linear congruence ax ≡ b(mod n) has a solution if and only if,
Consider a linear congruence a ≡ b (mod m), Choose the false relation from the option given below:
Choose the false statement:
Choose the linear congruence which has exactly 3 solution modulo 3
For any integers a and b, and positive integer n, consider the following statement: Statement: 1 If a ≡ b mod n and c ≡ d mod n then a + c ≡ b + d mod n. Statement: 2 If a ≡ b mod n, and c is a positive integer, then ca ≡ cb mod cn Statement: 3 If ab ≡ ac mod n and if gcd(a, n) = 1, then we have b ≡ c mod n. Which of the following statement is/are correct.
If a is a whole number and p is a prime number then according to Fermat's theorem:
Find the non-negative remainder when 4165 and 250 are divided by 7
What is the remainder when 220 + 330 + 440 + 550 + 117 is divided by 7?
What is the remainder when 331 is divided by 7?
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